Any other ideas on different wiring techniques?

Take this free advise at your own risk, I'm not an electrician.

14/3 has three conductors and one ground (black, white, red). I think
you mean 14/2, which has two conductors and a ground (black, white).
Do not count the ground for guage/conductor designations. I doubt you
need 14/3 on this circuit.

For a bathroom GFCI circuit I would run 12/2, install a 20 amp breaker
and all 20 amp rated equipment on the line. If you have a hairdryer
look at the wattage and divide by 120 to get the amperage draw.
Probably about 10 amps? Now figure that a 20 amp circuit is really
only designed for an 80% load (16 amps). Now figure that the light
you're installing will draw 1-2 amps. On a 15amp circuit you are now
drawing an 80% load (~12 amps), with no room to play safely. On a 20
circuit you still have some room to plug more stuff in safely.

If you are still doubtful then go to the library and ask to see the
2005 NEC, or a residental wiring manual based on it.

I would run the 12/2 from the bath to the breaker panel, not from the
panel to the bath. This way you can do as much work as you can using
the lights before cutting the power to the panel.

Cut the power to the panel before opening the box to wire the circuit
and have someone stand a few feet away from you with a flashlight so
you can see what you are doing. And if something should happen to you
they can call 911. No kidding...