Hi there. New house. 1 light on basement stairs. It is a 12-3 wire with a 3 way switch. I found the junction box. I am feeding wire from the junction box to another 3 way switch at the exterior door of the basement and now I want to run 12-2 wire from the switch to the lights on the ceiling. How do I do that? Also a 30 amp breaker on a 200 amp breaker box. How many 60 watts recessed lights can it hold before blowing the circuit? Also how many outlets can I put on another 30 amp circuit?

The thirty amp circuit questions- Zero recessed lights and zero outlets. Thirty amp branch circuits are not allowed for these uses in residences.

I can't speak to the 30Amp circuit, but 12 ga. Wire you can only use a 20 amp breaker. To figure out how many lights you could put you need to figure out how many amps you would be using. A=w/v I believe this is the formula that would work for you. If you have a 20 amp breaker.. . Divide watts by volts (110 or 220) to get you there. You won't want to use all of the 20 amps possible. You'll find it will trip the breaker often. If you'd want to you could probably put 30-35 on a 20 amp line. If you take the watts of the bulbs (60) multiply by the qty (30) you get 1800 watts. Take 1800 divided by 120 volts = 15 amps which you shouldn't have any issues with.