Batteries

At this point I just buy and use Eneloops. Good quality rechargeable batteries. You can by them in kits with a charger to get stared. People say the Amazon Basics rechargeable batteries are rebadged Eneloops too.

Eneloops are nickel-metal hydride (Ni-MH) rather than alkaline. They have a slightly lower voltage (1.2v), but maintain this longer than alkaline retain their 1.5V. I've never encountered a device that wouldn't run on them, but it can happen.

Testing

There are cheap battery testers online for ~$5. Probably the best way to go, as they do a good test because they put the battery under a bit of load. Simple enough insides you can fix yourself if you need to.

You can also test with a multimeter (mine is a budget $30: Digitech QM1321):

Reclaiming