What SSD interface/form factor is compatible with my 13" MBP (Mid 2012)? I have an old MacBook Pro (13", Mid 2012; 5,400 RPM HDD) that I want to bring back to life with an SSD. 

The options I've been exploring are the 2.5" SATA SSDs—am I looking for the right component? I just realized there's mSATA, not sure if that's what I should be looking for.

Thanks!
Yes! A 2.5 inch SATA SSD like this one from Samsung or this one from Crucial or this one from Western Digital will work.
(Note that those three are just examples.)