Well good for ya bro, love to see some H2s getting dirty! I cannot tell you how close I got to pulling the trigger and getting a used H2 for light wheeling and towing my camper.
I would suspect that for lifting purposes, you will be looking at the same things that go on Tahoes, since your suspension is nearly (if not 100%) identical. Most of us on here won't know much about lifting them specifically but can answer generic questions.
Lil' bling won't kill ya, first thing I would do is put on rockrails, black would make more sense so you do not mess them up, but make sure they are STRONG and not really thin/dentable "steps"
I believe you can get a winch that bolts in there, that would actually be my #1/2 recommendation along with the rockrails.
Then...I wouldn't lift it at ALL...I would trade tires and put on there either BFG M/Ts or Goodyear MTRs or similar. This will get you start on a decent road tire and light duty trail tire.
I "think" you probably have a rear locking diff, if so you are now set to wheel probably anything you would really want to anyway.
I hit URE a few weeks back in a stock Wrangler with 225/75 tires, but I do have a locker in rear axle. That allowed me to crawl everything I attempted, and avoid the harder /taller stuff I would have gotten hung on.
Welcome, enjoy....