I think we all have different ideas what punchy is, do you have a reference for the sound you like?
The quality of the pickups is not necessarily a limitation, many cheap ones sound just fine. The sound has a lot to do with their placement, so you should focus on that first (and wiring second). You can later upgrade pickups if you want.
Browse these forums for custom builds and modded basses, people have tried many configurations. A couple threads are even dedicated to three pickup basses, which can be an interesting approach. There are some sound samples. Then there’s YouTube... Anyway, the point is, try to get a good idea of what might get you close to what you want.
Just from the top of my head, a few options I’d cosnsider promising:
- J/MM/P, with MM in the traditional Stingray position.
- MM/P/J, with MM and P slightly more towards the bridge, and J towards the neck (from traditional positions)
- MM/J/P, with MM and J in traditional positions or slightly towards the bridge, and P in the extreme neck position...
Then again, two pickups are typically sufficient and imo look better. Or just one pickup! So think carefully what you want to do, and don’t do too much. One alternative is a swimpool rout, try all combinations till you find what you like, then build a pickguard/top to cover it... you can later build a new body too...