Looks like I am going to break down and buy some new shoes but I am confused, even after reading a hundred threads on wheels/tires.

Truck is 2006 4x4 Lariat Screw, mainly used for highway driving/ hauling 4 wheeler around.
Adding Autospring level kit also.

Deciding between these two rims...any suggestions or thoughts?

Both are 20x9, one with +35 offset, 6.63 backside, the other with +35 offset, 6.38 backside.

Questions:
1- What do you think about the rims?
2- What would be the best size tire (and a good brand) for those 20's, with enough meat on the tires to take up space in wheelwell? I dont really want a low-profile tire since I go off road a little with the four wheeler.
Thanks in advance for your help...

 

Nice! If you want an all terrian tire, I'd go with a 305/55-20 (33x12.50) Nitto Terra Grappler or BFG AT KO. If you want a street tire, I'd look at a 305/50-20 (32x12.50).