I am wiring my basement and have a spool of 14/2 as I was told this will suffice. Will it be fine for 3 way switches, recessed lighting on dimmers, etc.

Who "told you it will suffice"? Did they do a load determination to see what you need? Are you planning to run this for outlets too or just lighting. You might have a electric heater that will take all of the capacity on 1 line. It will not work on 3 way switches, you need 3 conductor i.e. 14/3 or 12/3. Tell us what you want to run.

I am using it for outlets as well. One breaker will have one light and one outlet. One with one light and 3 outlets. One with two Bathroom lights, and 1 GFCI. One with 3 lights on a 3way switch. One will be with 5 outlets. Entertainment room will have recessed pod lights (8) in groups of 4 on two dimmers.

14/2 cable is listed for 15 amps. 15 amp circuits are used for general lighting and general receptacle loads. It does not matter whether they are in the basement or elsewhere in the home.

As Ma0641 is telling you, we really need to know what type of circuit you are designing. For example if you are using a light controlled by two switches, 14/2 will not work. It would have to be 14/3.

However, if you are using a multi outlet circuit you are limited to 12 amps. For example, a double receptacle would be considered a multi outlet circuit.

You CANNOT use it for the bathroom GFI. That must be on a 20A circuit which requires #12 wire.

In addition to the sound advice you have received already, keep in mind, all the basement outlets, lighting and receptacles, need to be Arc Fault protected, there needs to be at least one hard wired smoke detector in the finished basement common area, and one in any room that will be a bedroom, all interconnected together and with any other smoke detectors that should be existing in the home.

Stan has already informed you that the bathroom must have a 20 amp circuit on #12 wire, which can serve the lighting, exhaust fan and at least one GFI receptacle in that one bathroom only.

As you, and any other reader can see, wiring a basement is much more than slinging #14-2 cable everywhere.