The tire on your back wheel right now will work great. Keep tire pressure up (check every time you ride). I have yet to disintegrate a tire and I've been using trainers since the fall of 1983.
It's free, will barely wear, and you can use your bike on the road without any problems if the weather is nice (tire slips/squeaks for about 1/2 mile if you have trainer haze on the tread).
Disclaimer: I avg about 160-200 watts on rides and don't do sprint efforts. Max wattage is about 1000 on the trainer for me, high pace is 400-500 watts for a minute.
cdr