Here's an easy chart to follow for tire diameter and rear end gear ratio.
http://www.4lo.com/geartable.html
Original tires on our trucks are about 30.6" outside diameter, and the original differential ratio is 3.91, so just follow the green boxes.
No, you don't get more power with a lower gear ratio (4.88) AND 37" tires---you'd have the same power as shown by the green boxes on the chart. What you gain with the gear ratio is lost with the big tires.
Don't believe their suggestion of better gas mileage when you're in the zone of the yellow boxes. On our trucks, the combination of the overdrive ratio (0.7:1), the differential ratio, and the OE tire diameter is about optimum for gas mileage. A higher effective ratio (lower number differential gears or bigger tires) usually means that the transmission is spending more time in overdrive with the torque converter unlocked, or in 3rd, so gas mileage suffers.
Ken