A couple of questions:
First, do you leave the boat in the water or use a trailer?
Second, if you leave the boat in the water, do you have a shorepower post at the dock or is it on a mooring or dock with no power?
An AGM Group 24 battery with a small charger should do the trick... given your very limited needs. The reason I said an AGM battery, is that they don't self-discharge as quickly... and they're easier to transport, since they don't have a liquid electrolyte to spill.
If you trailer the boat or have it on a dock with no power or a mooring, I would recommend you get a small AC 10 amp smart charger and use that at home to charge the battery. Just carry the battery back and forth and connect it when you need it.
This should suit your barebones style...
However, if you want to make things more convenient, and the boat is at a dock with a shorepower setup... install a proper ground power inlet plug, 120 AC panel, and one GFCI outlet, and then use a small waterproof AC charger to charge the battery. You should also install a DC breaker panel and wiring with a battery switch. The advantage of this, even though it is more work, is when you want to do work on the boat, you have easy access to 110VAC via the on GFCI outlet.