a b13 motor should work with a b14 auto tranny, or g20 auto.
the only major differences between the b13 and b14 is the intake manifold, and throttle body location.

everything else should be similar though.
but youre still going to have to change motor mounts, and other things.
if youre wanting to stay auto, the sr20 isnt going to be very fast, and i still maintain that for what it seems you want to do with the car, id put in another ga16de.