Re: What size battery?
Depending on what type of battery you have under the hood I would upgrade to the biggest size you can physically fit. I would just go to a local parts store and have someone try different batteries to see what group size fits, then order whatever battery you want in that size. Some recommend Optima yellow tops, Deka, or Kinetik. Whatever tickles your fancy. If you're still having voltage issues (I doubt you will with a 120a alt and a good battery) you should consider a second battery.
For fusing a second battery you will need one within 18" of the under-hood battery, and another within 18" of the other battery on the main power wire. 300 amp fuse will be more than enough for you.
2002 Mazda Protege5
Rockford Fosgate 1050S
2 10" Powerbass M10s