12 spaces is OK for this, but 20 or 24 spaces would not be out of place
A 12 space panel is a bit small, but OK for this job, given that you'll be using main lugs here. I would upsize to a 20 or 24 space unit though if at all possible -- as Harper said, "Spaces are cheap, regrets are expensive."
I'd stay in the BR line, however
Whoever recommended you a GE panel, though, was silly, and that breaker P/N isn't even a valid Eaton part number! (The correct Eaton P/N for a 50A two-pole breaker for that panel is CL250, BTW, and the corresponding native GE breaker for that would be a THQL2150.) I'd just get something like a BR2424L125G for this (provided it's indoors -- the outdoor counterpart is a BR2424L125R, but you'll need to field fit the grounding bar yourself in that case).
Don't forget the details
Make sure you pull the bonding Z-strap in the new subpanel, and also torque all the panel and breaker lugs to manufacturer's specs with an inch-pound torque wrench!