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which battery specification can suite my application.
NIMH batteries are a popular consumer item, and it's easy for a merchant to sell you a sub-standard product with a claim it meets big-time specs. You can expect to pay between $30 and $60 for a 6-cell pack rated 6 Amp-Hours. It is important that you purchase from a reputable source. Shipping costs can add another $10.
NIMH are not indestructible. You need to be careful how rapidly and how long you charge them. You need to be careful how far down you discharge them.
It is still reasonable to consider a 6V lead-acid battery. You might find them carried in a motorcycle shop.
A 12V supply will charge okay, but you must make sure the charge rate is suited to the Amp-Hr rating. If necessary you must limit current with an inline resistor. You must charge for only a certain amount of time, stopping when the battery is full.