Have you put drainage holes in? If you haven't yet, look into creating a false bottom (perhaps with the lid) and putting a side drainage hole about 3 cm from the base so you have a wicking pot. I have a couple of tomato plants that are growing in wicking pots at the moment (they have a wire trellis around them and I think mine are about 25L). Zucchini will probably be too big unless specifically a "patio" variety. Your lettuces, rocket will do well and I could see you using 1 pot per plant for things like the brassicas. All my strawberries are grown in rectangular wicking pots on the fence line, they would do well. Herbs - i have coriander, mint and parsely in a pot but have grown basil before.
Anyway, hope this helps.
I grow a lot of veges in containers. I grow more in sacks than buckets, but we all use what we can get hold of easily and cheaply. I have grown Garlic, Tomatoes, Potatoes, Cabbage, Leeks, Bok Choi, Carrots, Kale in small containers with a good degree of success. Mostly I grow in a mix of sandy soil, horse manure, and compost. I also grow long rooted things like Carrots in 75 dia PVC pipes in good quality potting mix without manures added. These then develop long straight roots and don't fork like they do in a rich soil mix. I have just tried ti upload some photos of this but the process is not working at the moment. I will add these later when the website gets itself sorted out.
Interested in the outcome of your experiment Stephen :)
Another thing so so easy to grow is water celery.Place into a smaller bucket or pot with holes your growing medium and plant in then put it in a bucket a bit bigger ,obviously your large bucket wont have any holes this will act as your water reservoir .I also grow a few types of mint and brazillian spinach in buckets with only one hole an inch up on the side to drain excess water.Good luck