Types of mountainbiking. . .
1) XC. Cross country. Hard to define, but it is an all-around discipline combining climbing with technical skills. Endurance is a key part of this sport as time in the saddle pedaling is much more than other MTB disciplines. Can be as simple as an unpaved bike path, or as radical as a NORBA XC race course. Hardtails are still serviceable, but the world is moving FS and disc brakes these days. $700 for entry level hardtail, $1,000-$1,200 FS.
2) DH. Downhill. Gravity powered top to botton, lift for shuttle assist bottom to top. Some pedaling required, but don't try to climb with these 40-50 lb. bikes. Lots of suspension travel on both ends and $2,500 to $6,000 for a bike that won't break after one season. Upper body is key to take the pounding. Racers like good acceleration, but races only last 2 - 4 minutes. Plan on expensive accessories like full-face helmets, body armor and lift tickets.
3) FR. Freeride. What is this? Activity or sport. Big drops, lots of air. Urban or wilderness. Technical. Bikes seem to be a DH hybrid, more pedaling, so lighter with more gears. Have fun with stunts, but may not go anywhere. $2,000 and up for a durable bike you'd want and can beat up.
You can have a blast on a hardtail, and even win XC races. You can ride DH on a hardtail, you just can't go as fast, and if it's an XC bike you'll beat it up badly fast. Lots of DH requires good equipment and mechanical ability to repair the stuff you'll break.
XC is a journey, an afternoon in the wilderness hammering with friends or exploring a new trail. Maybe it's riding the bike paths with the wife and kids. It's versatile and a good place to start.