I raced crit on Zaffiro Pros, 23c. I also commuted, trained etc on them. This year will be Michelin Pro 4 or an equivalent since the LBS carries them.
A 23c tire is fine, some prefer 25c. I think (and just IMHO) if it'll be your first year, I'd focus more on learning the ropes rather than equipment. Crit racing (again IMHO) teaches you bike handling skills and confidence, something that a $1800 set of wheels will not compensate for.
Others may disagree, but with your bike on a Rock 'n' Roll trainer, you obviously have the desire to do this, but (Merlin may disagree here) I think that being in the pack is a heck of a lot different than just spinning pedals, even in a group ride.
My first time out, I made a LOT of tactical errors, once I overcame those, I learned how to "read" what was going on, when to expect attacks, etc.
I know he has more experience than I, just my 2 cents.
A true warrior feels fear but says **** it