well, start with working out what sizes you need each of the pieces to be. I have limited experience, but I can remember buying my first lot and being in the same position! Tick each piece off as you account for it. I take a piece of chalk with me and mark it on the board if it is one i am going to take. If for example i can get 3 legs from a board, i divide it roughly into thirds by eye and put an L in each section.
I try not to have to get everything from a massive board- I would rather take 2 6" boards than a 12" one if possible- it is easier to handle, and tends to be flatter. Sometimes of course you need the larger one! Add a bit to each for wastage so you can trim to size later etc. Then look at the timber in the stack. you want something that looks straight, reasonably flat and not twisted. Take your time and you will soon see what to look for. If you look at the end of the pack, you can target boards to look at. If you want a 6" one, look for a 6" one and see what it is like. You want, ideally a board that is know free- unless you want the knots as a feature- or failing that enough area on the board so that you can take the bits that you need and avoid the knots.
The yard should knock off the defects from the measure. Not all do- I bought Prime Euro Oak recently, and they just used the fact that it had been classified when imported and so everything was in spec. I think that was a bit naughty, and I didnt realise until I got it home, but it wasnt actually bad stuff. There is a thread of mine called "yellow stain", or something like that. In that, somebody links to a defect document that shows you some of the potential problems- worth a look. If the wood looks good, then it probably is. Beware that sawn hardwood often looks grubby, and may have some water stains, marks, paint on the end of boards. This all comes out when planed but it can be shocking when you first see it. Look on some of the WIP threads- the box making one somebody used some chestnut I think that looked rough in the sawn form, and fantastic when planed- that shows the difference well.
Dont be rushed, but likewise dont try to spend all day finding a perfect board. You will send yourself crazy, and it is only oak. If it was walnut for a gun stock etc then it is a bit more tricky!
Why not put a picture up of what you plan to build, with some sizes on and I will talk you through my thought process on buying the timber. It works for me, others may do it differently.