In general, any variety with 'early' in the name or description will be a good choice for containers as these are often smaller sized fruit or roots and therefore plants.
Also in general, herbs are your 'gateway' drug to container gardening. Almost all the herbs you want to grow are easily grown in our climate. Basil, thyme, oregano and all of those are very easy in containers. Basil is a summer annual while cilantro is a winter annual. Most of the other herbs are perennial and will provide you with delicious flavor all year round. Almost all the herbs are in the mint family are very, very easy to grow, almost thriving on neglect. If you are new to veggies, start with herbs. If you are new to container gardening, start with herbs. They are insect and disease free.
Try to plant flowers among your veggies, make them look good! There is no reason to have your veggie containers look like utilitarian gardens when you can have nasturtiums hanging over the rim, or alyssum or lobelia. Add marigolds in summer, calendula in winter or any plant you think will increase color and appearance. The bonus is the flowers will help deter pests and will attract pollinators. It's a twofer!
Artichoke – one of any variety in a 15 gallon container – you won't get more than four or so chokes per year except in perfect conditions. Green Globe, Violetto are two varieties to try.
Asparagus – a perennial is not a good candidate for container culture. Asparagus roots are planted in late Fall early Winter here and will not produce a harvest for two years. In most container culture, it is simply not feasible.
Beans – you can get one meal of beans out of a 6x6” container of bush beans. They have shallow roots, so six inches deep will suffice, but 8-10 would be better. Beans can have a bush or climbing habit. Bush beans are usually more easily managed in a container, but pole beans need a large container (more depth too simply to balance with the weight of the top growth combined with poles). All beans can be planted among other plants in a container as they supply nitrogen. Do not plant with tomatoes. Some bush beans: Royalty Purple Pod (can be planted earliest because, unlike most beans, will germinate and thrive in cold soil), Blue Lake or Kentucky Wonder are the standards; I love Romano beans and for a yellow bean, Roc d'Or. Pole beans: All the above (except Roc d'Or) have a pole habit counterpart, in addition, Scarlet Runner is a wonderful container climber with some of the showiest flowers in the veggie world. Drying beans are not your best choice for container production unless you have some large containers to hold enough plants to make it worth your money.
Beets – only in a container at least 12” deep and more would be better. Don't expect a huge crop – put in a beet seed about two inches equidistant from one another and the container edge and you should do OK. Remember, when thinning beets, the tops are marvelous in salads. For a red beet, Early Blood Red or Detroit Dark Red are both good; for a real taste treat, Golden and Chioggia beets are super. Cylindra, in a deeper container can be planted closer together because their roots are more carrot shaped.
Broccoli – of all the cabbage family plants, broccoli is one of the most productive in containers – and it's pretty too! One plant per 16” of diameter in an 18” container. If you can find Nutribud, it is THE premier broccoli variety for containers, beyond that DeCicco and Calabrese are good second choices.
Brussels Sprouts, Cabbage and Caulifower – much less performing in containers. Brussels Sprouts are long, slow crop, demanding of nutrition and if they don't get it their way, extremely susceptible to aphid infestations which are murder to deal with when harvesting. Early Jersey Wakefield is a good cabbage – any of the smaller 'early' cabbages are good choices – any cabbage that takes longer than 80-90 days is going to be a hassle and somewhat less than ideal. If it's described as 'late,' forget it. Cauliflower is, as Mark Twain once opined, “...is just cabbage that went to college,” and has the same hassles in containers. Early Snowball is your best choice if you wish to ignore me.
Carrots – need a helluva root run so the best way to plant carrots is in with another plant needing a deep root run – like tomatoes. The only container carrot to defy that rule is those little ones like Paris Market that are all of two bites long. In with tomatoes, and 18 to 24” minimum depth, you can try any of the ordinary ones like Scarlet Nantes or St. Valery.
Chard – is not grown by the Swiss and didn't originate there, so I'm moving to call it simply 'chard.' This is an easy to grow plant, if given a bit of room (18” minimum) and you'll get a long harvest over the cool season. Most chards will hang on for two years if you're lucky. Five Color Silverbeet (silverbeet is the Australian name for chard) is a delightful mix of five different plant colors, Red Rhubarb, as the name suggests, is a lovely red ribbed variety. They are all good and will all give you a good harvest.
Collards – are acceptable as container plants. Vates and Georgia Southern are fine choices – they need a minimum 18x18” container per plant.
Corn – oh, for show, I guess you could plant one or two, but corn does not really lend itself well to container gardens – you really need a minimum of 20 plants or so to effect a good stand to pollinate – with poor pollination will result in ears that are not well-filled. If you want the show, plant a few Bloody Butcher plants in a 10 or 15 gallon container and fertilize heavily. They will get to 14' tall and people will be wowing all over them.
Cucumbers – another difficult one in a container, but... the little Persian cucumbers are smaller plants and good choices for your container garden. Most of the others, if you can put a large trellis for them, you can grow most of them – leave Lemon Cucumbers out – their plants are just too aggressive! Cucumbers need consistent moisture.
Eggplant – any variety of eggplant does well in containers, the plants are fine in anything more than five gallons, although the smaller varieties will be more productive. Casper and Pingtung Long are really good choices.
Kale – is a good choice for winter containers. One plant per five gallon (about 18”) in a drift of 3 to 5, depending on your kale consumption or tolerance, will be a good supply for one or two folks. Lacinato is the one chefs rave about, but all of them are good choices for us. It really prefers cool temperatures.
Leeks – are a challenge because they take so long – like garlic. You can plant them in with other plants as a companion to repel insects (like garlic) but don't plan on a helluva harvest. Blue Solaise is one of the smaller ones – but it still takes 100 to 120 days.
Lettuce - and all salad greens are some of the best container garden plants going. They are shallow rooted, play well in close quarters and are quickly grown without much fuss. Choose your lettuces according to the season – there are lettuces that are heat tolerant (All Year Round) and lettuces that love cold weather (almost everything else). There are butterhead lettuces (that are way too expensive at the market) and looseleaf lettuces of many different colors. All of them fun and easy. I can't make it through the lettuce selection of many seed catalogs without ordering way too many packages of lettuce seed! All of the salad greens, endive, escarole, and spinach are just as easy and fun.
Melons – a lot like cucumbers only worse, in terms of space. I don't know that one can get a decent harvest of melons of any kind – the vines are long and need to be trellised and need space. Look for any melon that is listed as 'space saving' or 'compact.' And good luck.
Okra – need a large container – a well grown okra plant will get six feet tall and is a gorgeous addition to any garden. You'll need a 10 gallon container for each plant, well-grown, will net you a bunch of pods. Red Burgundy and Clemson Spineless are a little smaller and better for containers.
Onions – for storage are not going to be a good and productive container plant. Grow scallions or Long Red of Florence or Red Torpedo (Tropea) and eat them fresh.
Peas – are a great container plant. Like beans, peas can be climbing or bush. Choose according to your needs. Remember the bush varieties will produce more of a crop all at once while the climbing will produce more peas over a longer period. Some of the varieties we've enjoyed include Amish Snap (climbing), Blue Podded (climbing) is a gorgeous SOUP pea... leave the peas to dry and use them in soup, and Dwarf Gray Sugar (bush) are all ones to try.
Peppers – are a wonderful container plant just like eggplants and they are very ornamental, if you leave the peppers to mature (all green peppers are just unripe peppers that would have changed to a color if they had been allowed to ripen). If you like 'em sweet, Jimmy Nardellos, Marconi and Sweet Chocolate; for the hotheads, Jalapenos, Habaneros and Joe's Long Cayenne are some ideas, but really, any one you want to grow will be happy in an 18”/five gallon or so container.
Radishes – are one of the easiest root crops to grow – give them 18” or so depth and you'll be able to eat fresh radishes in about a month. French Breakfast, Watermelon and all others are easy as you can get in growing a vegetable. If you like radishes.
Squash – needs a big container. Summer squashes, the zucchinis, crooknecks, all the squashes with soft skins that eaten fresh, are large plants, but if you have the space and give them a 10 or 15 gallon container, you'll do fine. They will probably get powdery mildew, so plan on a short season or start another plant every other month as long as the weather is warm. Once the mature plant has mildew, yank it and start over. For summer squash, I like Lebonese (light green) better than the dark ones, but the dark ones are more productive. WINTER squashes are a whole 'nuther critter, being the hard skin squashes (pumpkins are a winter squash) and take a long time. They are probably among the largest plants in the garden, so, you need a lot of space and perhaps a sturdy trellis. Personally? I'd pass.
Tomatoes – like the other members of that family, are container garden stars as long as you stay out of the really big heirlooms. You will have a lot of luck with all of the saladettes (the smaller two to three inch tomatoes) and cherry types. In my book the paste tomatoes – especially the determinate types – are your container gardens top performers. Burbank's Slicer, Rutgers, Siletz, and Taxi (a yellow) are all determinate and will not get over four feet hall. Almost all cherry tomatoes will be larger plants as will most of the saladette types. In the latter camp, Juane Flamme, Shady Lady, Black from Tula, Cherokee Purple and a million others will do just fine.
Watermelon – find small fruited ones and good luck. These can be grown more easily than winter squash, but they still take a lot of room. A trellis is highly recommended. Small Shining Light, Stone Mountain, Petite Yellow and Golden Midget are candidates for your experiment.