Here's my two cents (or dollars) worth. Please note that I was an avid mountain biker a few years ago. The straight answer is: You're not going to find a $200 bike that is good for long distances. $200 will get you a cheap, crappy bike from Wal-mart that's about it. Your best bet is to find a local bike store and talk to them. Tell them that you want something cheap, good for long distances, AND most importantly that you want to test ride some bikes. You'll be amazed at how different bikes feel and handle. Over a 50 to 100 mile trip you'll REALLY notice the difference!
Here are my suggestions:
1) Buy a steel-framed bike over aluminum or titanium
Reason: aluminum is lighter but stiffer, stiffer typically equals sorer on a long ride, titanium is too expensive for you
2) Buy the lightest bike that you can afford
Reason: weight is your biggest enemy, more weight equals more effort especially when climbing hills
3) Rotational weight is MUCH more important than non-rotational weight
Reason: Rotational weight (e.g. wheels, chain rings, pedals) are amplified by centrifical force.
4) Make sure the bike fits you
Reason: If you put too much weight on the seat or too much weight on the handle bars something bad will happen (see previous posts) this can also lead to carpal tunnel syndrome, etc... The solution to this is seat height, stem length, handle bar angle, handle bar style, etc...
5) Expect a "good" bike to be a minimum of $500-800. You should ride some more expensive bikes to get the feel for a good, quality bike.
6) Save some cash for good quality gloves AND good padded biking shorts.
