so, my main question is> is it ok to use wood as a frame?
Any frame is going to give slugs a place to hide, more or less. I'd say go with the wood. You could plant some tall perennial grasses or grains along one side, or at one end, to serve as a beetle bank. That can help with slugs:
https://en.wikipedia.org/wiki/Beetle_bank.
also, any advice on starting vegetables, specially those that would look good and entice my patron on allowing me to expand the gardening area?
I like the John Jeavons style of starting seedlings in flats. You can use containers or pots you already have (no need to build boxes like in the videos), and you can easily grow as many seedlings as you need. Here's a
video about it.
As for varieties, I have no clue. Try to find a reference book for your area, or local seed company, or even better - find a local gardening club or gardeners and ask them what works well in your area.
Best of luck, and congratulations on starting to get your hands dirty!