I'm still rather new to mountain biking, but the following are my priorities for a bike (in no particular order):
- Weight
- Fork
- Tires
- Proper fit
Right now I have an old Specialized Stumpjumper single speed and a really heavy Marin geared MTB. Even though the Specialized has like 45mm of suspension travel, it's so much easier on my body because there's less weight being thrown at me. 10 pounds makes a huge difference. The fork I put on my Marin (Rock Shox Judy J1) is a cheap pile of junk with no damping. Sure it has twice the travel, but it's way too bouncy and it weighs twice as much! If you upgrade your fork, shop carefully and get a good one. I think tires are really important too. I always get the widest tire possible for my mountain bikes. Ask what other people are running before you buy the tire that looks cool in the store.
To answer your original question, I don't think frames are a huge deal. As long as it's not super heavy, and "feels" good to you, it's fine. I think a good fork would make a big improvement on that bike.