Which 50 amp breaker do I need for my old Eaton panel?
Eaton has two breaker lines: 


the residential grade (cheap) one, BR
the industrial grade (good) one, CH.  


This is CH. It is an excellent panel. Hold onto it!  

BR will be placed more up-front because it's more popular.  If you stop there and give up, that's the trouble.  Most likely the store also carries CH.  Look for it: the narrow package and distinctive beige handle is the giveaway. 

Expect to pay under $12 for this CH240 or CH250 breaker, which should be readily available. 

You asked about other brands of breaker.  You cannot put J. Random brand of breaker in your panel, even if it seems to fit because it doesn't actually.  You must use breakers either manufactured by the OEM for that panel (e.g. Eaton), or competitor breakers that are UL-listed (technically, UL-classified) for that panel. I'm not aware of any classified breakers for CH.  It wouldn't save you any money, and the beige wouldn't match!