Quality factors relevant for getting a replacement battery (MacBook Pro (13-inch, Mid 2012))
There are a number of different battery manufacturers out there; the problem with figuring out which one is the better of all the others is you never know which one will perform and which one won't.

Pretty much all will have the correct specs and will connect to your device whether that be a MacBook Pro, an alarm system or a back up UPS.  What I have found in my many years of experience is to go with the vendor that offers the best warranty.

Generally speaking when I went "cheap" I ended up having to replace the battery much sooner than expected.  If I spent a little more on a battery with an 18 month or 24 month warranty, I usually got 3-5 years out of it which is the norm for me.

Egoway and Lizone are two batteries that I would recommend as replacements for your particular MacBook Pro.

Replacing them is pretty simple too.  You basically remove the 10 scews on the back and remove the back cover to expose the logic board and battery.  Remove the battery connector from the logic board (on the right) and pull the battery up by the tab.  Just reverse the steps to install the new one.  

The pictures below give an abridged version of this procedure, but you can find the full detailed instructions on iFixit.com