Basically, you're looking for oak which has been air-dried or kiln-dried, assuming you can find 4in. thick stock, of course. Green or unseasoned oak is what you should avoid, at all costs! If you're buying English oak (generally sold with one if not two waney-edges) then the moisture content will almost certainly be higher than the equivalent of imported oak (European or North American)... You could be looking at somewhere between 14-18%, depending on how well the wood's been stored and how long it's been lying around for.
With furniture going in to a home with central-heating, you ideally want a moisture content of 10-12%
before you start machining. This can mean stacking the wood indoors for several weeks, checking with a half-decent moisture meter, every so often.
Buying 4in. oak is going to be expensive, as you'll probably have to buy a full length, from which you could cut a lot more than four table legs! You could look at your cutting list and, if your looking for rails at a sawn size of 4"x1", for instance, you could try to get these from the same length of 4in. oak, instead of buying more 1in. boards... But, this is a more expensive way to do it and there is the risk of unleashing stress from inside the timber (wood often has a higher moisture content inside, particularly with thicker timbers).
You could try laminating them from 1in. boards but, you've either got to join for lengths together with
perfect 45° mitres down both edges or, unless you can get a perfect grain match, you'll need to veneer over the two faces (carefully!) to hide the joints and glue lines. The choice is yours.
Really, a moisture meter is what you need to determine whether or not your timber is ready to work with. Even if it's vastly over-sized, I'd be reluctant to starting ripping rough components out until the m/c is closer to 14% - I made this mistake a few months back with some beech and it split quite badly! :? Oak is more stable but, at more than £50/ft³, it's not worth the risk! I have access to a decent moisture meter at college for now. I did own a cheap one (£20) but, it wasn't terribly accurate and is now destined for the bin!
Unless there's a forum member closer who could lend you a meter then I'd suggest you look through some old posts in the Buying Advice forum, where the subject of 'moisture meters' came up over the summer.