Read this thread for info on some of the popular entry-level bolt ons:
http://www.crownvic.net/ubbthreads/ubbthreads.php?ubb=showflat&Number=1320971&fpart=1
I doubt you want to swap the engine or get into the heads/cams/timing it. Most actually pull the engine just to swap the heads.
That said, I would start with gears (3.55), dual exhaust if you don't have it, a Marauder airbox and MAF, and a tune.
The steeper rear gears will make the largest impact, the car will feel like it lost a couple hundred pounds. I use 3.55s on my supercharged Marquis and they feel perfect. I had 3.27s and 2.73s prior. Your 2000 TC has 3.08s stock if non-Touring.
Later on you can replace the nPI intake manifold for a PI intake manifold for a little more power or do some of the other small upgrades (ie underdrives)
Swapping to the PI intake yields very impressive gains and is a very simple retrofit.
And yes, you will pass emissions with a dual exhaust as long as the cats are in place and you have no existing CEL/codes.
I think your best bet would be to go with a set of ported PI heads and the most mild cam Comp Cams makes. With that setup you'll still have a smooth idle and good vacuum and you should see torque improvements on the low end.
Actually he would notice less low-end torque with those. PI heads make more power, but not as much on the low end as nPIs.
Installing PI heads on his nPI block will also cause a compression bump which is good for even more power than a normal PI block/heads, and would help a little with the PI torque loss, though.
FRPP / Mustang shorty headers ARE NOT worth the hassle to install on a panther unless you plan on more significant upgrades. They are prone to warping flanges and leaking. One of the primary tubes needs to be 'massaged' with a hammer to clear the steering shaft. Only the BBK shorties require cutting/welding the tube in a new position.
Take a look around the manifold and note how TIGHT clearance is there. Installation is a b~tch!
As for a manual tranny swap - there is a guide on my webpage documenting my buddy Ian's conversion on his Crown Victoria to a T-45. If you used a different manual trans it would be mostly the same provided it is from a Mustang ('96+ - ie 01+ TR-3560)
That should be possible with a 3 grand budget IF (and only if) you are doing the work yourself.