can't see any reason to go with anything bigger than a normal battery, there are less electrical consumers than a standard car, the biggest being the starter.
I would get the battery tested, it's the weakest link normally, and it is likely to have been stood, which they don't like, while the car was up for sale. however there are other things that can cause the same systems, such as poor earth's and connections, a common failing on kit cars.
You will have to find the output of the alternator you have fitted for advice, kit cars are rarely "standard" and anything could have been fitted.
regards