My allotment is a real haven! Bit of a different climate here though. Anyway, my advice is as follows:
- Radish is I think the single most easiest vegetable to grow.
- Then I'd go for whatever greens are the most expensive and suit your climate - perpetual spinach, pak choi, lettuce, rocket, have always done very well for me.
- Finally - soft fruit... strawberries and raspberries, the later especially are basically weeds.
The later two I grow purely because they are the best in terms of how easy they are to grow in relation to their expense in the shops (maximum smugness factor when you're picking $2 of greens a day and $5 worth of fresh fruit every day in summer, and basically just grazing your plot.
Once you get the bug you'll take it further I'm sure...this is the most inspiring 'homesteading example' I've ever seen... although you might have to move to proper rural Japan to make it work:
I think the above might fit well with your ethics....
But it all starts with:
- radish
- greens
- soft fruit
In yer back garden!