Here are the battery chemistries I pay the most attention to:

NiCd sucks.

LiCoO2 AKA ICR (you probably know them as Lithium Ion batteries) are used in most cellphones, laptops, and so on. Great capacity and cycle life, with low self-discharge rates. Prone to "vent with flame" when damaged or discharged too quickly. Don't use these unless they have built-in protective circuitry. I use these in most non-AA/AAA devices.

LiMn2O4 AKA IMR are used in vapes and other high-discharge uses like high-performance flashlights. Significantly safer than ICR chemistry but has less capacity and cycle life. Most think they don't need protective circuitry. Great in high-discharge devices. I use these in one specific device.

LiNiMnCoO2 AKA INR supposedly combine the best features of ICR and IMR. I don't have any of these.

NiMH is the chemistry used by Eneloops. I use these extensively in place of primary (non-rechargeable) batteries in AA and AAA devices.

None of these (other than NiCd) have a "memory" effect and handle top-up charges well.

Long-term storage of rechargeables is best, supposedly, at around 40% of charge to prevent degradation over time. I keep most of my rechargeables in "ready to use" mode, fully charged or nearly so.