Rechargable batteries are fine to use in Wiimotes, but if you want a longer term solution try looking into a battery pack built for the wii.
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The Wii remote does not come with its own rechargeable battery. Although there are third party rechargeable alternatives available, the charge times for these batteries differ depending on the brand and model.
Wii remotes need two double A batteries to work.
The Wii Fit Balance Board (if you can get one) uses 4 AA batteries.
AA
Wii remotes run on 2 AA batteries but if you can get a pair of recharable batteries then yes you would need to charge them. (Pick your brand carefully, some batteries run out fast!)