To some extent, we have failed to mention a few things to our OP.
(1) While lithium batteries are always preferable IMHO, they do not come in basic AA battery form in the 1.2 to 1.5 volt range unless we are dealing with special non rechargeable lithium batteries. So if the device in question requires batteries in that size and voltage range, the only real current rechargeable option is Nickel metal hydride or nickle cadmium.
(2) As a rechargeable battery type, IMHO, Ni-Cads are damn near worthless.
(3) NI-MH aka nickel metal hydride batteries are far better for recharging in my experience. But this thread fails to mention that they come in basically two types.
(a) The normal higher capacity battery NI-MH that carries with in the fact that just sitting used, it loses 3% of its charge every day. Meaning in a month or so, its pretty well dead. But for a photographer who expects to go go forth with freshly charged batteries every day, and return with the batteries used up, the fact that each regular type NI-MH battery hold some 20% more charge means fewer batteries to lug around.
(b) The special NI-MH type battery that loses far far far less charge just sitting unused.
At the end of a year or so they can retain 80-90% of their charge. And that is the type I have standardized on. Great for things like clocks, TV remotes, and all kinds of photo devices.
(3) As for the last thing on battery chargers, I am not sure I am right, but its seems to be true from what I read. Because Battery chargers also come in two basic types. There is the so called 1 hour fast charger, that feeds a depleted battery high voltage initially, and then the smart ones reduce voltage to top the battery up. But its the dumb fast chargers the damage batteries by feeding them too much voltage for too long. Then there is the slow trickle chargers that never uses high voltage, but instead of one hour, its takes 24 hours to charge the batteries. But as long as I don't exceed 24 hours on a depleted battery, I have experienced no battery damage. I got more time that I have money. But one day I imagine I will break down and spend the $30.00-$50.00 bucks to get a smart charger.