How many outlets can be on 1-20 amp breaker with 12-2 wire? Also how many lights on a15 amp breaker with 14-2 wire?

Depends on what you plan to run. May be only 1. For general house wiring there is no limit. However you typically would plan for 80% of Max permitted. 120 VAC at 20 amps =2400 watts. 80% =1920 watts. Same for lighting. What is wattage planned? 120 X 15=1800 watts. X 80%=1440. Biggest issues are running heating devices or motors for more than 3 hours continuous. That's where the 80% comes in.

Mainly a media room and laundry. Just trying to figure out how many breakers to put in. I'm going to run lights separate from the receptacles.

I would run the laundry outlets separately, the media room separately and then the lights. 2 X20 and 1X15 amp. If you need space, use the slim breakers.

Might I suggest you get a good book on home wiring.
Asking vague questions online will not get you all the correct info you need.

Laundry areas have strict rules as to what receptacles can be on the circuit, among dozens of other relevant codes and requirements.

Might I suggest that you go through the equipment that you are planning to install and calculate how much amperage you will need to supply the equipment. Once you know what the load will be, multiply it by 125% (1.25) I do this because this type of equipment is often on for more than 3 hours at a time and while they are not true continuous operation loads, I want the extra safety margin.

Once I know what my necessary amperage is, I then plan for the needed circuits.