jameso’s advice is sound. It might also help you to understand some of the marketing cobblers that surrounds mountain biking.
The following are fairly meaningless labels but will help you grasp what the people trying to sell you stuff are talking about:
XC (cross country)
100-120mm travel. Light, fast, good all-round mountain bikes. May be a bit race-orientated and less comfortable at the top end of the range
Trail
120-150mm travel. A more capable all-round bike. Slower uphill but more comfortable on long days and better on tougher downhill stuff.
AM (all mountain)
140-170mm travel. More focused on going downhill and hitting jumps and drops. Still capable of being ridden uphill but slower and with more effort.
Freeride
160mm+ travel. Jumping off cliffs and generally endangering your life.
Downhill
Loads of travel. Racing down v. steep hills with big jumps and generally endangering your life.
I’d recommend something from the first two categories. And, personally, I think a hardtail makes more sense to start on. But it’s no biggy.