ITP Holeshots are GREAT on the trails! I've got a set of 20x10 or 11 for the stock 10" rim and they are great for the trails. Running 13/42 gearing and it'll go up anything it could ever want.
For paddles a good TOUGH paddle with decent bite is a Dune Slider. It's a V-tread and real tough. I've got a set of 21x10-8 on ITP rims. Again 13/42 gearing on the LT, 13/46 on my ATC110. I've yet to trail them but I did tear up a feild with them lol.
You could also look into the Paddle Masters. They are really aggressive but heavy. But very tough from what my uncles told me.
For dirt play, again the Holeshots' or Maxxis Razr's would do really well. The Razr's are way harder. An 18" would be good for non-rutted dirt play but 20's would be best.
Also, Kenda Fast Trekkers are a pretty good tire but they are really hard and it's hard to get them to actually hook