The Pirelli DRC's are a nice crossover tyre if you're running a road bike but have a harder compound in the middle that you'll not gain anything from as this is track only.
I'd be looking at Supercorsa SP's as an excellent all round tyre that heat up quickly, have plenty of grip and be a good stepping stone to slicks.
Once you're happy you can keep enough heat in the tyres for the session, you'll be able to feel the benefit and added grip with the extra cost of full slicks.