Choosing a long-travel cross-country fork I ride hard-tail cross-country for recreation (Specialized Hardrock with disc brakes). Recently, my fork got damaged and now I am looking for a replacement. My current(now previous) fork has 80mm or 100mm travel, I'm not sure.

My goal is to make the bike a little bit more "down-hilly". I believe that this can be solved by a long-travel fork, for example 140mm. The goal is to both improve the suspension and change the geometry to compensate for the slope of the trail. However I am completely at loss as to how to select a new fork.


Does the fork travel correlate with the total length of the fork arms?  
What other characteristics are important? There is significant variation in prices, although the longer travel seems to cost more. My target price is about $220
Longer travel will change the bikes geometry. A 140mm travel fork has 60mm more travel, therefore needs 60mm more clearance. To get this, you need a smaller wheel or longer forks. Presuming you are sticking to the same wheels, you have to raise the sheerer height. The effect of this is a more relaxed sheerer angle - changing the handling for the bike. 

Personally I would not do it. The Hardrock is not a down hill bike, and never will be. With your target price, as you have observed - you get a lower travel higher quality fork.  This would be far better. The fork will be stiffer and more robust, probably lighter and likely to be more adjustable. 

In your situation, I would put on the highest quality shock I could afford, and forget about increasing travel. I recommend 100mm to 120mm max. A well setup better quality short travel fork will walk all over a cheap long travel fork on all but the most extreme DH rides, and the compromise when not on those extreme DH rides is, well, extreme......