Keep it simple. Have tires closer to 2 finger widths across than 1 finger width. Or larger.

Make sure your wheels are properly tensioned. Your current wheels are probably fine once tightened up. You can pay someone to do it...will probably be in the $50 to $100 range to rebuild your current wheels, or you can buy a $10 spoke wrench and $50 tensionometer to do it yourself while reading up on wheelbuilding on the Sheldon Brown website. It is time intensive....but relaxing and really not all that difficult. Dishing tool would probably be handy as well. Still...either way you're looking at around $100 to get the problem fixed. At your weight, you may just have more truing problems than other regardless of what wheels you have, but having them tensioned properly will dramatically reduce the problems i think.