Most of my garden is in containers. I've grown tomatoes, various herbs, peppers and chilis, cucumbers, various types of eggplant, cantaloupe, watermelon, various peas, summer and winter squash, beans, and strawberries in containers on my patio and porch.
I use SIPs containers (sub irrigated planters). You can make your own in big buckets, but I use the City Pickers planters sold at Home Depot. I've also bought one garden patch GrowBox. I prefer the City Pickers because they give instructions that don't require future purchases. I've just followed those directions for the other box, but it hits me the wrong way to try to make people forever dependent on buying specific products to use their box. The boxes are all sort of expensive but last several years and truly make gardening almost hands off other than filling the reservoirs. I have had one container develop a leak, so I converted it to a top watering container. I don't think SIPs matters that much if you're willing to really watch the soil moisture, but it's the only way I've successfully grown cucumbers in containers. In regular containers, mine have always turned bitter when the weather got hot (something they do when distressed).
I have had great luck with small tomatoes. Large ones, I just can't grow in the ground or in SIPs. I've had San Marzanos and heirloom tomatoes in SIPs containers that looked like they were doing great, and they all got blossom end rot at the last minute. I suspect the roots found the water chamber underneath and started sucking up too much water, causing them to not have enough calcium. But idk.
I live in the pnw, so I was shocked to find melons that grow well. They were miniature--personal sized cantaloupe.
I used to grow just crazy amounts of chilis and peppers--lots of hard to find varieties, too--but don't anymore. For me, they grow great in containers. I grew a lot in non-SIPS containers (which have very specific fertilizing instructions) and found that using some sort of "bloom and blossom" type fertilizer helped the plants have enough fruit. I wish I could remember the name of it, but we're out and I can't remember what it was called.
As for choosing what to grow--cherry tomatoes are pretty easy. Herbs are a big win, too, since they cost so much in stores. If you eat any veggies that aren't easy to get where you live, grow those (for us, that's usually holy basil, fenugreek, and Asian eggplants, but everyone would be different. I'm lazing out an only growing the eggplant this year.)
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