1996-1998 mustangs use the non PI heads (performance increase). These mustangs are easily beatable with your current car. However the 1999-2004 mustangs have the newer heads and will most likely be a good race for you, it'd be close. Also 1993-1987 5.0 notch back mustangs should be a good race as well.
As for what to do next. Well considering your mileage, i'd be leary of doing much to that engine. I'd say do an LS1 swap, or rebuild the current LT1. You can get LS1 crate engines pretty cheaply, an LS2 is also a possibility, or any LS series engine.
I'd recomend going onto a F-body forum and asking those people. I am a mustang owner myself and my knowledge of LT1s and F-bodys is limited, however the same principles apply for both f-bodys and mustangs or any car when it comes to modifications.
Based on your mileage i'd say get a new motor, either a rebuilt LT1, or an LS1. There deffinetly will be a lot involved in converting to a different engine such as the LS1. A computer change, possibly you may need a different trans and or bellhousing, all differnt wiring, possibly a fuel pump and fuel lines change (if one is return less and the return fuel system), or you may need a higher capacity fuel pump.
To do the LS1 swap, go to a junkyard or on ebay and look for a rear end totaled out LS1 carrying F-body (1998-2002 firebird or camaro)
The simpler thing would be to just get a lower mileage engine out of the exact same car, 1995 Z28 / 1995 trans am. Then just upgrade that engine.
Working on F-bodies is a pain in the butt with the engine compartment arangement. B/c of this i think swapping the engine would be ideal. Get an extra LT1, build it up on an engine stand and get it all ready. Then jack your car in the air and lower out your engine (F-bodies you lower the engine instead of picking it), then put the new built engine in the car ( a one day project) this will also limit down time.
Commence rebuilding old engine, and use it as a spare, or sell it after you rebuild it. Rebuilding it will be educational and good practice.
recommend making sure you have a lot of tools. Impact wrench, air tank, proper torque wrenches, the highest jack stands and floor jack possible, engine stand (with wheels), chery picker, torch, get the GM tech manuals for your (CD versions are available) screw the hayne/chilton manuals they are useless and lack key information.
Oh and the things to do to the junkyard low mileage engine would be:
The best cylinder heads you can afford, these are the heart and soul of an motor. With high fuel prices a good breathing motor as opposed to force induction (superchargers, turbos etc..) is the best option. You will also want to pick out a cam and valve springs, rocker arms, and valve sized all at once. You probably can buy this from a vendor online and they can help you chose a package. You will also want to upgrade the intake manifold as well.
If 450-500 hp isnt enough for you, you may need forced induction. A turbo will cost the most but offers the most possible hp you can ever get out of that engine, as well it is the most efficient (better mpg). A supercharger is simple and cheap and gets the job done, but not the best approach.
Another option would be to just take the new motor, put a supercharger with matching cam and blow the doors off of just aobut anyone.
Also you could just blow up the current motor with a supercharger, wait for it to die and have a replacement ready to go. Most likely the supercharger wouldn't break.
I've heard that the LS1 heads fit on LT1s, but i maybe mistaken. This is also an option. I do not recommend physically upgrading this old engine, as it may damage the heads or cam if t his engine fails. This is why i recomend just boosting the current motor with nitrous
or a supercharger till it explodes, or replacing it with a built motor.