A hard tail has front suspension, so your specialized would be called a fully rigid if the fork is rigid. There are some great mountain bikes these days, with so much variety that one can get a bike to specialize for a specific area (cross country or free ride/down hill being the extremes in the spectrum), or a bike somewhere in between depending on the kind of riding you want to do. There is a good quote relating to this spectrum from Keith Bontrager that goes something like this..."high strength, low weight, or low price. You can only pick two". However, price is relative and a decent new mountain bike hardtail starts at around $1,000 (low price). My bike has a decent weight to strength ratio, but is still fairly heavy (~30lbs), and cost so far about $2,000. I have about $600 worth of upgrades planned within the next year. However, my bike is meant to get rough, and can handle pretty big jumps, drops, and other abuse. It is also heavily modified/customized, and would have been much cheaper to get a better bike in the very beginning, which wasn't an option at the time.
If you have great trails around, and are serious about getting into MTB, I would recommend browsing some biking forums (or better yet, talk to local riders) to get an idea of what kind of bike is best for the kind of riding you want to do in your area.