I keep my chain sparkling clean and well-lubricated without removing it, or using a dedicated chain cleaner. I use Simple Green, a rag, and Pedro's Ice Wax.
As for a trainer, I just got a Cycleops Mag at REI for $119. I believe they are still on sale.
Michelin Pro Race 2-I've not used them, but they have an excellent reputation. However, if you've been running a 25, going to a 23 may give a slightly rougher ride.