How about a quick guide?
First off, what sort of Mountainbiking do you want to do? Without defining or restricting niches, MTBing is all things to all people. It ranges from cindertrack and towpath bimbles to full-on XC/marathon racing, from enjoying the occasional loamy forest path to full on big-air, balls out freeride. Fully padded stormtrooper downhill racer long distance bike-packing? Do you want to ride local bridleways and fire roads, or go exploring cheeky bits of the countryside that some would hesitate to walk up? Do you want to be a weekend trailcentre visitor or do you want to spend your leisure hours armed with a map and compass/GPS and go two-wheeled rambling? (Whatever you do, just don't tell me you want to fit a rack and panniers and use it to commute in the winter because your trip to work includes three potholes........)
In the UK we are blessed with factors which offer us immense choice in what we can do. We have a MTB setup which has shaped the evolution of certain types of bike. As a result the market has been shaped to offer us a massive variety which some may find daunting. The market itself is very confusing unless you know certain things to look out for, not least because some manufacturers build and name their models to suit a particular style, and while a lot of them share components and outward appearance, some bikes are better suited to their intended purpose, whereas others can be modified or adapted to suit yours.
To answer your original question, a Race hardtail is designed with shortish, taut travel to maintain traction on uneven surfaces. 100mm Travel is typical, and to explain that, the fork has a stanchion which slides in and out of the lower leg which allows the fork to compress by up to 100mm on hitting a bump or landing off a step or jump. Once it has compressed, it will return to its extended length again, ready to absorb the next hit. How easily it does that depends on the type of spring it's fitted with, and the method of compression damping it has. More later. In the right hands Race or XC hardtails are capable of overcoming quite steep and demanding drops, steps and so on, but they also take some taming. Think flighty thoroughbred. The riding position is arse up head down, with frames designed to give a strong rider the advantage on climbs, but the payback for a less experienced rider is a less composed descent. To keep your weight forward on a climb is good thing, but the same position for a descent is like staring into the abyss.....there's nothing between you and the next faceplant over the bars. In Race/XC world, typical frames have a steep head angle of 71/72 degrees or so (that's the angle between the fork leg and the wheelbase) which make the bike sharper to steer, easier to climb on, and seat angles of similar steepness which puts your body over the cranks to deliver power. This power and precision is great on the flat and uphill, but at a cost of downhill stability.
A trail hardtail has longer travel fork. That fork will typically give between 120 and 140mm of travel. It will also have a slacker head angle (66- 68 degrees usually, although market blurring will mean some are as steep as 70 degrees). The seat angle will still be sharpish to allow for reasonable climbing ability, but overall the bike will be slacker and more confidence inspiring on downhills. Think of being in rather than perched on top of the bike. The slacker geometry, longer wheelbase of a Trail Hardtail makes it far more beginner friendly in my opinion. Have a look here
http://www.pinkbike.com/news/bike-frame-geometry-2009.html
A further sub genre is the hardcore hardtail, built around the UK (Peak and Pennine branch) MTBers love of technical trails. Big, rocky, nadgery descents demanding long travel on burly, bombproof frames that will take massive levels of abuse and courageous riding. See this post for more
trail bikes vs cross country bikes
I'll make an assumption based on my own experience (let me know if I'm wrong!) , and that is that you fancy an entry level bike that will be suited to bridleways and local paths/trails which you intend to ride with a view to building up to more challenging terrain and intend to visit a trailcentre or two to build up your skills and confidence. You may not know this now, as you have a budget in mind that will take your readies and launch you into your voyage of discovery, but you are about to delve into a wallet-emptying world of upgrades and market hype, fraught with glossy magazine features on how the next upgrade will turn the weekend warrior into a riding god.
However, if I were to be asked for one piece of advice, it would be to spend as much as you possibly can on your first bike. Sounds daft, but the current market is flooded with all sorts of stuff that looks and sounds like it should do what it says on the tin, but the entry level market has some holes in it. To keep prices low, manufacturers spec forks that are badly or completely undamped, heavy, budget drivetrains and crap tyres, low-budget wheelsets and woeful brakes. They cheerfully announce that their "lightweight" offering is only 14.5kg, which in "serious MTB world" is the sort of weight that you would expect your fully equipped 180mm travel full suss with all-mountain wheels and tyres enduro bike to weigh. Massive weight won't trouble you on a towpath, but start trying to ride that sort of thing on a red trailcentre route, and you'll soon question the parentage of the people that talked you into buying it. (Dons flameproof suit)
