Jenyphur -
The OEM Adventure tire size is a 285/70-16. This is a 33" diamiter tire vs a 32" tire for the basic setup. Depending on how agressive you want to go there are a variety of options. Just remember the more agressive a tire, the louder it may be and it may have a shorter life.
Some people have tried out and had success with tires Nitto and Toyo tires in 33" sizes. Some other people have had great things to say about Pro Comp XTerrain tires in a 315/75-16. This is a 35" tire which will give you more ground clearance and a more agressive look.
Do a search on these, check the H3 technical discussion page and don't be afraid of asking questions. There are people here with TONS of experience (I won't claim this) and if you show that you did some homework before asking they typically can be a wealth of knowledge.
Good luck!
