Pre-2005 PC’s have a single group 31. Starting the generator is not a problem.
Deep cycle means the battery can handle being used up and recharged over and over without degrading the usable capacity. When comparing different brands online look for the highest CCA and reserve minutes, then buy the heaviest battery, not the most expensive one with the longest warranty. More weight = more lead = more capacity. Check NAPA auto parts and Walmart first.
For the house battery(ies) CCA and reserve amps have little meaning. They deal with vehicle starting capability. Also, vehicle engine starting batteries are designed to almost always fully charged. Using them as deep cycle batteries will quickly ruin them.
Deep cycle batteries are designed to be discharged down to about 11 volts and then recharged many, many times. That is why they are used in electric carts, like golf carts and RVs.
Deep cycle batteries are rated in amp hours. AGM batteries are far better than wet cell batteries where you need to keep checking water level in the cells.
If you use 6v deep cycle batteries, you need 2, they must be put in series to get 12v the amp hours will not change. If you use 2 12v deep cycle batteries, they must be wired in parallel and the amp hours will double.
Yes I use expensive 6v AGM deep cycle batteries from Lifeline batteries, they are expensive ($600+ for both) but are 5 years old and still hold a full charge. NO corrosion in those 5 years.