you can go with a mountain bike or hybrid bike for trails at parks, but i'll be honest with you...90% of the time, its not gonna last long, and you're going to have an expensive garage ornament.
mountain biking is fun. i'm a road cyclist, but i enjoy it. i don't own a mountain bike though. know why? because you have to load your bike up, go somewhere just to ride, and i'm not gonna buy one that i know i will get sick of that process any time i want to ride it. i go a few times a year when either friends are going and have an extra mountain bike, or when the local shops/dealers (Trek, Specialized) have demo days and you can go out and ride the fuck out of a $4-5k bike for a couple hours.
my vote is to find a decent level road bike. my now rain/winter bike is a Cannondale CAAD8 i bought a couple years ago. you can probably pick one up now for ~$500. put on some 25 tires (for your weight), get a bit more comfortable ride. a road bike you can go from your front door, and go pretty much anywhere. hell, last year, i left my house near easton, rode to my family reunion at the delaware dam (~35 miles), rode part way home, stopped at the bike shop, did a group ride with some friends, then back home.
this would actually be pretty decent for you, just swap out the tires to get a smoother ride. those 23s jacked up to enough air for your weight are gonna be a rough ride
http://columbus.craigslist.org/bik/4377721281.html
and since you asked about sizes, if you go with the road option, a 58cm will probably be best for you @ 6'1, but you'll probably be fine on a 56cm as well