1.) Windsor swap. Fox k-member/mounts, drop in a Windsor SBF of your choice, carbureted. Stroker kit, H/C/I and/or spray. Fox based PS pump and alternator. New fuel pump/regulator. Minimal investment.
2a.) 4V swap (carbureted) Drop in a 4V engine (5.4 even better). Spray optional. Carbureted intake manifold, and either a distributor swap or digital ignition box. Hydroboost setup from a new edge for clearance. New fuel pump/regulator. I think it was bulloch27 that managed to hit your goals for low $$$ with this.
2b.) 4V swap (EFI). Same as above, but with all the EFI trimmings. This pretty much means you need a donor car for the ECM and all the harnesses. It can be done cheap if you can find a cheap donor car. 2V is an option with this route, but then you need to drop more money on ported or aftermarket heads.
Regardless of what you pick, you're going to want/need an automatic transmission, preferably with a suitable stall and shift kit to your combination. Also an 8.8 axle with a well matched gear set to your combination. Slicks help a lot. If you're going to launch hard on them, especially with a manual, look into a 31 spline axle upgrade. Upgraded LCAs are a good idea as well, and shocks/springs.
Or if you've got a screw loose, make that V6 a 4.2 and turbo it for shits and giggles.
11 seconds could be had with an m112 swap on your 3.8 with an adapter plate from jeff limmex. That can get you around 400 hp depending how far you want to push it. Also can be done easily for less than $1500
Then you would either want a 8.8 or to built your 7.5 rear with some better parts. Sticky tires and get some decent suspension. 11s wouldnt be out of the question