I am using a Vee Rubber folding tyre on the turbo trainer and been pleasantly surprised at the durability of the tyre. It was bought from Halfords in the UK for the miserly sum of £10, very cheap for a folding tyre. It also has a puncture protect belt. Haven't actually tried it on the road but it has lasted ages without any shedding on the turbo. Initially at first use you get some black residue on the turbo roller for the first 4 or 5 turbo sessions but then it clears and runs very clean. It is sold by Halfords under their Bike Hut brand.

Some initial black residue on the turbo roller for the first four or five sessions but you just wipe it off. After that runs very clean without much shedding. I lose somewhere between 7% and 8% speed compared to something like a Michelin Lithion on the turbo so I reckon this is a slow tyre. Doesn't matter on the turbo but might bother you on the road.

Vee Rubber road I'm 6'0 (182cm) at 213 lbs. Using Vee Rubber 700×25 at 1800kms so far at 80-90psi, no punctures and still at almost 50% tread at rear tire and 80% at front. Rotated them now for longer use. Grip is great, confident 45deg corners and bends at 40-60 kph Highly appreciated.

I little more weight than racing models but for everyday training these are great for training with fast clips.