I am looking to buy a rechargeable battery that can provide me enough power to power 2 6V .8mA motors for a decent amount of time (maybe about an hour per charge) and was wondering a few things.
NiMH, 2100mAh or higher, 5-cells should do.
(The motors doesn't draw 0.8mA but 0.8A which is 800mA!)
Don't use lithium based batteries for your first project, NiMH will be fine and they aren't dangerous like the Lithiums can be if not treated absolutely correct.
First, if I buy a battery that is rated at something like 6V and 2200mAh, does that imply anything about its current? By that I mean does the mAh rating influence the maximum amp output of a battery, or is the max output unlimited in terms of mA, and only limited by how long it can supply that amperage?
The capacity rating is the 5-hour discharge rate
. This means that a 2200mAh cell can supply 440mA for 5 hours
. If your current draw is higher than 440mA, the capacity will be less - the higher the current draw, the less capacity (and v.v.).
My second question is regarding connections. I have noticed that many batteries come with specialized connections (e.g. Tamiya style connector, JR Connector, ect.) but does this mean that they should not be connected to smaller circuitry?
No, that just means that they can handle more current.
It's like with nails - you can use a large hammer on a small nail, but a watch makers hammer won't impress a 9" nail.
Furthermore, is it possible to isolate the positive and negative leads of the battery to use as a direct power source?
Not sure what you mean here?
If you mean to "disable" the battery while using a mains driven power supply, isolating just the positive lead will be enough - theis can be donw with a switch, a diode (which will introduce a voltage drop) or a more elaborate circuit.
My last question is one of pure mechanics: (http://www.sparkfun.com/datasheets/DevTools/Arduino/Ardumoto_v13.pdf) can anyone tell me if the board has a maximum voltage/amperage input to power the motor outputs? Thanks for all the help.
Did you read the schematic
you link to??
It says Max input: 18VDC
Current is only drawn as needed.