Hmmmmm. Depends. You don't actually say what you want "sound wise".
If you're after something that sounds just like a P or a J, only shortscale, then you're unlikely to get that in an off-the-shelf instrument. Shortscales have a character, a sound, and a feel that's all their own. People who want something that sounds like a Precision usually buy a Precision.
Fitting very bright rounds will help of course, but they won't stay very bright for long and that could prove an expensive route.
Very generic advice would be to start by buying a cheapish Mustang just to make sure that you get on with shortscales and that they actually solve your problem.