I know this thread has talked a lot about Li-Ion type batteries but I wanted to throw in a couple of points and ideas on the lead-acid types.
Many years ago (and much before I got into HeaterMeter) I outfitted my outdoor shed with a small solar panel, charge controller, and storage battery. Its sole purpose, at the time, was to operate a homemade (Arduino-based) irrigation controller and associated RV water pump for a number of fruit trees and garden beds that draws water from a series of connected rain barrels. It is completely "off the grid" as far as electricity and water is concerned. I have since expanded its use to power my HeaterMeter and some LED lights.
When it came to selecting a battery for solar power storage, it is general practice to select lead-acid batteries which are rated for "deep cycle" - meaning they can withstand going from full to near zero capacity on a regular basis. Regular car/tractor type batteries are not rated for deep cycle, as their main use is short-duration high draw use - ie. starting your engine in subzero temperatures. Repeated near full power draw on a regular car-type battery will eventually kill it. The battery I use is an "Auto Craft" brand from Advance Auto. It's a deep cycle marine battery which I believe has about 70 AH of capacity. If I remember it was roughly $80 online, but Advance Auto constantly has 25% or $30/off type of coupons that can be used to bring it down.
These batteries are easy to maintain and keep charged. In the "off season", I use a cheap Battery Tender to keep it topped off and working properly.
I recently did a 12 hr pork shoulder cook using the HM and the battery hardly broke a sweat.
As others have mentioned, lead-acid's drawback is weight. While I only move the battery from the shed twice a year, I just have it "installed" on a small inexpensive hand cart so it's no big deal.
