It's 4 years now that every spring I try to create my apartment-compatible garden!
I sow seeds I've collected the previous year or I transplant small plants that I've bought in the supermarket. It requires time (that I don't always have), will and a bit of physical efforts but the reward is incredible.
Sweet basil: I'm Italian and I use sweet basil in many recipes. Especially during summer time you can use it with tomatoes (which I'm growing too), mozzarella, beef carpaccio and in many other ways to prepare quick but tasty plates.
Anise basil: a weird but extremely interesting variant that gets along with grilled swordfish and tuna fish. Noteworthy the combination with strawberries (the plant I have, doesn't set many fruits but the few ones are amazingly sweet), red wine and sugar.
Rosemary and Thyme: Any BBQed meat and (almost) any fish.
Parsley (please grow! please grow!): mainly to prepare sautéed mussels/sea shells, but also for tomato sauce (penne all'arrabiata want parsley on top!) and more.
Italian chili peppers or peperoncini (which unfortunately I'm struggling to grow this year): EVERYWHERE!
Peppermint: I love it in gin tonic!
In addition, I have a lavender plant from which I hope I'll collect a lot of floral buds for my winter lavender sachets, a tiny Drosera plant that eats mosquitos and an osteospermum hybrid plant the properties/usage of which I ignore but that is very nice and decorative!