Any recommendations you receive will likely be what others have bought, and mine will not be different. For the past 10 years, I have been very happy with
Eneloop Pro 2500mAh NiMH batteries for my speedlights and remote triggers. The AA batteries are a bit pricey for a 4-pack, but when I had eight Nikon speedlights and Pocketwizard triggers mounted in various locations, I didn't want to run the risk of a set of batteries going flat during a photo shoot.
For normal household applications, I use the
Eneloop 1900mAh NiMH batteries. These hold a decent charge for TV remotes, clocks, cordless phones, and wireless computer mice and keyboards. I have an HP 48GX calculator that has been using the same batteries for almost two years without a charge, and I use it several times a day. There is a version of the battery packs that come with plastic cases for storage.
I use the
Maha MH-C800S charger because it can charge eight AA or AAA batteries at a time, in any combination, and has a reconditioning function.
The Amazon links are for reference only, as there might be other sources that suit you.