Rail passes
 

Is it cheaper to buy a rail pass for the country (on raileurope, single country pass=3 days in 15 days for $158 US) or to buy train tickets separately in Austria? (I'm over 26 years old)

It depends on your itinerary. Try it at:
www.railsaver.com
to see what it suggests.

If you can understand some German, you can check prices on the Austrian rail site:

http://www.oebb.at

Where and when will you be traveling??

Greg

I will be staying in Vienna but I'd like to go to Salzburg, Innsbruck, and maybe St.Anton and Graz, from mid-June to early July.

OK, you will not be traveling around enough to require a pass. Just buy as you go. Second class will be just fine. The Vienna to Salzburg route can get pretty crowded at times, so buy your tickets in advance if possible. Have a good trip.

Greg