Vibrating Motor

what motor? what is it vibrating? leaf spring or 3 point vibrating mech?

If it's your standard 12mm silver motor, I'd pump 2.0v to 3v. I'd go 3v. It gives you the full mount of rpm.
Daniel's secret black mamba motor, you're good with 1.5v to 2v you're good. Nothing more.
 
Both a AA and a AAA deliver the same voltage, which determines the speed of your motor. the AA has more capacity, which just means it will last longer. 12 AAA's wired in series (end to end) will deliver roughly the same voltage as a large truck battery, both will spin a motor at the same speed. The truck battery will spin it much, much longer.

Sounds like you're going to want to wire your 4 batteries as 2x2 or even 4 in parallel to keep the voltage down within motor range.
 
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