I hate those 2 battery systems where you have to use both
If the yard is less than a quarter acre or even a half acre, a cheap battery mower should be sufficient. My 14" Sun Joe is perfectly adequate for most size lawns. The battery that came with it is in its third season, and there are no problems. It's a 4 Ah battery, though a 5Ah upgrade battery is also available. Sunjoe is good for a cheap mower if you don't want to spend too much money. If you're willing to spend a little more, there are better brands that others have listed.
Any yard where a push mower is sufficient, a cordless battery electric mower will also be sufficient.