Dear Chuck and mid-60s Buick fans,
Boy do I have a lot of questions. Seams like there is not a lot of aftermarket support for this car.
Sadly the earlier Buicks don't get a such interest so the reproduction parts are as numerous. Do you know "da' usual suspects" when it comes to Buick parts?
There are many smaller suppliers and lots of parts from other GM cars will fit. You need to ask these guys for specifics.
So what is the biggest tire wheel combo you can fit on the front and rear. I tried looking it up but I'm getting all kinds of different answers.
Unfortunately it depends on how bold you are. Guys are getting away with various 17" combos. Hopefully other guys will jump in on this one. Otherwise perhaps you should ask this question specifically in this topic:
http://65gs.com/board/index.php?board=24.0
Hang in there, it is a bit intimidating at first, but the 1964-65 Buicks are well-supported compared to many other Buicks.
Cheers, Edouard 
I just put a set of 17x8s on my 65 and have no issues. Its close but no contact. Tires are 245 wide and measured height is just under 26". BS was advertised at 4.5" but I measured it just a hair more than that but still close.
I know of one car that has fit 275/40/17s out back and it is very close but I think he has done a small bit of clearance work too. If I wanted to get every last mm of tread under the back with a perfect offset I could probably squeeze some 285 or 295 wide tires in back.
I have some pics up in another thread in introductions and new members area with a link to my pics. My car looks lowered, and it is, but its because the springs are worn out

It is at very close to what I want the finished height to be so that good, its there for the wrong reasons though. Hope that helps some.