If your aircraft has only one wheel per main gear, buy the highest quality tire available (even if you think it's more than you can afford), and change them early and often. With tires you usually get what you pay for, and while all flat tires are equally flat, your biggest concern at that moment is that the flat tire remains attached to the wheel, and doesnt shred, etc as you roll down the runway trying to stop. If it comes completely unglued and leaves the airplane, damaged wheels and struts (or worse if things really get exciting) are more expensive than the money you save by scrimping on tire cost, or letting them wear to the point that they decide for you when their useful life is up. Apparently, they do this at the highest speed, at night, and on the wettest, narrowest, shortest runway possible.
I remember our Westwind tires were 18-ply, rated to 210, and cost about $700 dollars each, but that was money well-spent considering each one protected $10,000 wheel and brake assemblies, struts, flaps (if things began to grind down), and against FODing an engine. Ones who have been unfortunate to have experienced incidents of lost tires say its a lot noisier than a regular takeoff or landing (and at this time I'd like to thank the aircraft designers at Israel Aircraft Industries for deciding to rest their 23,500 lb. bird on only one tire per side, thereby making this appreciation for good rubber possible).
Of course, this doesn't even touch on the costs involved if such a loss of directional control caused a high-speed runway excursion, forcing an impromptu and eye-opening "Bagel Bomber Baja" ride through the pucket brush. Whether at 60 knots in a Skyhawk or 140 in an Israeli Love Machine, I'd rather be in my Jeep for that kind of "moment".
Of course, dual-wheel main gear tires and nosewheel tires aren't quite as critical, and you could get by with less quality if you swear to change them when there is any question as to how much life is left in them. No matter what kind of tires you buy, always make sure the wheels are inspected during changes as per maintenance manual.