I am finishing my basement(2 b/r, ba, den).what size circuit breakers and wire gauge should I use?

I assume we are talking about receptacle and lighting circuits.
In that case, you can use 14 awg wire with 15 amp breakers, or 12 awg wire with 20 amp breakers. The advantage of 12 awg wire is that you can have a larger load on the circuit; the advantage of 14 awg wire is that it is cheaper. 12 awg is usually preferred for receptacle circuits.
However, you really need to check with your local codes. The bathroom receptacle(s) will have to be a GFCI. You will probably need AFCI breakers for at least the bedroom circuits. Also, some codes only allow 12 awg wire in certain cases. Best to check with your local codes.

The square footage will dictate the min quantity of circuits. 1000 SF would need two 20 amp circuits, for example, except bath. All circuits outside of bath will need to be AFCI protected. The bath will need at least one 20 amp circuit, which can serve the GFI outlet, lights, and fan. Any electric heat will be additional circuits.

Each bedroom needs a smoke detector, and the common area on that level needs one, all interconnected, and, hopefully, to the other detectors in the home.