Wheel size

What is the biggest size rims i can put on the rear of my 63 galaxie without rubbing wheel wells? width and height?

rubbing isn't about the rim size itself, it's about the tire/ wheel's combo overall height, some rubber band tires have thinner sidewalls than others so using those thinner sidewall tires could allow you to use an inch or so bigger, I'd have to say that 16" or 17" would be plenty big enough though, you could probably run an inch or inch and 1/2 or so wider than the tires you have now.

It won't do much good for anyone here, or anywhere else for that matter, to toss you a number. At best it might be an informed guess if they've had a similar car and have played the game. You've got the actual car, you should measure from what you've got to what it will accept. Not all cars were built the same, so tolerances will vary. Also, if your car has had any body work done in those areas it may have more or less than what it started with. Besides tire size, you also need to consider rim width, and offset.

Here's a calculator to help get you started on the tire size;
http://www.mindspring.com/~cinque/test/tirecalc.html