If going with flooded LA then a pair of 6V Golf Cart battys in series is an ideal deep cycle batty for house use.
see
https://marinehowto.com/what-is-a-deep-cycle-battery/
If you go with AGM then (at least per East Penn) their AGM line battys have the same plate design and perform both deep cycle and starting for GCs and starting batty. Look at specs and choose size and AH desired. - No advantage of 6V in series w/ AGM and you can parallel multi 12V to get more AH and still be able to take a bad one out of the system if/when it fails where 6V GC must be taken out in pairs.
Sams Club East Penn AGMs are reasonably priced and I've had good luck w/ many of these.