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.

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):

• As usual, have the black lead in 'COM'.
• Put the red lead into the port with 'V'.
• Set the dial to measure DC (⎓) voltage (V). Mine has AC and DC on the same position.
• Touch the black probe to the negative part of the battery.
• Touch the red probe to the positive part.
• AA, AAA etc. cells will show 1.5V when full. 9V batteries will show 9V!