That gear set up results in a 3.5:1 gear ratio, IMHO, I would drop it to at least 3.8 like x-bird did. Below is a link for a jackshaft gearing calculator I like to use, play around with the gear numbers and find what looks good to you, but remember, the engine gear is limited by the manufacturers, so you might only have 1 or 2 options. I like using a bit bigger gears on the jackshaft to be able to use a smaller gear on the axle, thus resulting in increased ground clearance.
As for the size of the shaft, I would go no less than 1" with quality pillow block bearings, and depending on the length, I might suggest using 3 support bearings to eliminate any flex.
http://www.fasttrackraceway.com/calc/