At $35 you can't go too far wrong, but that is not an uncommon price for a Schwinn Varsity.
It might be a little unusual to find one that old, but it doesn't really make it that much
more desirable. They aren't really all that much fun to ride. If you need a bike to do a short
Sunday afternoon ride, this will do. But if you are doing anything like 20 miles, this one will
wear you out.

Bob Hufford has done a lot of work putting Schwinn publications on line.
This for example is the dealer price list from 1965. You can see the Varsity was the
low end of the "Men's lightweight" category. The Paramount (at the very end of the
list) brought a great deal more.

http://www.geocities.com/sldbretail/1965/65rtlprc.html

If you want to learn about Schwinn's you will do well to spend some time on this
site. There are some good short articles here:
http://sheldonbrown.com/chicago-schwinns.html

And of course you can search bike forums!