Bathroom remodel electric questions
It sounds like you have or had knob and tube wiring that might have been converted,
 which consists on a Hot and a Neutral With no Ground (which is needed for GFCI, but 

sometimes use the Neutral pigtail to mickey mouse false ground,).

*You can add a ground with a wire to copper pipe from sink’s water supply or run to basement) 

14-2 wire is rated at 15 amps MAX 

12-2 wire is rated 20 amps MAX

If you splice or run off a 14 Gauge to a 12 Gauge you must treat it as a 14 gauge 

The higher the gauge the smaller the wire weakest link being 14 while using 14 to 12

If you are rewiring the whole bath and rooms then 12 gauge is the sanest answer

12 Gauge handles 15 or 20 amperes 14 should not be more than 15 for safety reasons 

(When using 12 on 20A breaker use screw terminal as opposed to tension insert)

Testing for a hot wire when there is no labeling on wire casing (sheath) use a meter on
 ~ AC

And use a ground from ground cold water pipe and then touch pos lead on each wire (they 
do sell polarity test tools also don’t always work with conversion wiring) 

The 110 – 120V reading wire is the hot

Hope that answers your question.

Sincerely BEAR