best tire size for mini tub?

Shortening the rear will depend on the rims you're planning to run. If you're going to run 15" rims, shortening the rear might be a good idea as it can be hard to find 15" rims with a deep backspace. If you're going to run 17's or 18's you'd be better off leaving the rear end the stock width, as most off the shelf 17's and 18's have plenty of backspacing.

And of course you'll need to do the 3" spring relocation for the mini-tub to do you any good.