Lots of questions there BB!
OK, in order (ish)
1) Rectangle good - make it as long as you like but now more than about a metre wide - so you can reach it from both sides without having to tread on it.
2) I personally wouldn't bother with membrane - it won't stop weeds growing on top of it and you really need to get perennial weeds out from under it. When we made our beds we double dug the area removing it all to a wheelbarrow. We turned the turfs upside down in the bottom, covered with cardboard then mixed the rest of the soil with compost and filled it. All compost is generally too rich for veg - they need soil too.
3) How deep you make the beds is entirely up to you - ours are quite high ~18" - but we're preparing for old age (which is catching up rapidly!

). A lot of people only make them the height of the boarding they've used.
4) It's really difficult to advise on what to grow - it depends how big a bed you're planning on, whether you want to grow a less of several things or lots of one or two. The HDRA site gives some good advice about all year round planting - using a rotation system. And if you search on here (box in top right corner) you'll find plenty of advice too.