Welcome to the 5.0 world.
I upgraded from Hondas too. Even though these cars are totally different, they're pretty straightforward once you get to know them, and they're easy to work on.
As others are saying, unless the engine is totally shot, I wouldn't worry about doing any rebuilding just yet. The 5.0's internals really are just as durable as any Honda engine's, they're known to go for a long time and take a lot of abuse before finally wearing out. If you keep up on maintenance these cars are really pretty reliable, despite what most import guys think. I'd just make sure any little problems are fixed first... do a full tune up, check your cooling system, check the brakes and steering. Make sure the car is in perfect stock condition before you get serious about modding, otherwise you'll just run into big headaches later on.
For the suspension, do you want something drag oriented or handling oriented? Either way, get subframe connectors first. These weld into your frame rails and stiffen the entire chassis. About $75-125 + install. I probably wouldn't bother with coilovers for your budget, just a good set of springs and shocks/struts. Bilstein, Koni and Tokico make good handling focused shocks/struts ($350-$550). Look at Eibach, H&R, and Ford Racing for springs ($150-250). When lowering these cars caster/camber plates are usually needed to help get your alignment set up right ($130-190). I'm not too well read on drag suspensions, but I see a lot of people having good results with the Eibach drag springs and Lakewood or Strange shocks/struts. If you're going for drag you'll probably want some beefier rear control arms to handle hard launches, at least the lower arms anyway. Make sure to inspect all of your bushings and replace anything that's worn out- with the age of the car most of them probably will be. Might want to just get a complete kit from somewhere like Energy Suspension and replace everything with urethane stuff.
All of the above will net you a very good basic setup. Most guys don't go any further for a street 5.0, but if you want to make it handle even better you can look into a panhard bar, and maybe even a torque arm for the rear suspension- check out Maximum Motorsports, their stuff is as good as anything out there & their site does a good job explaning how these parts work. Expensive but worth it if you want the best handling possbile.
For making horsepower you have even more options. Most people get a heads/cam/intake combo. You can spend anywhere from $750 for ported stock heads and intake with the stock cam, to $2000 or more for aftermarket heads and intake and a custom ground cam. And that's not including the new gaskets you'll need, nor bigger injectors, mass air flow sensor and throttle body, possibly a fuel pump and a fuel pressure regulator to support the new air & fuel needs. Boost is always another option, there are many different bolt-on supercharger kits avalible for these cars, and turbo setups are becoming more and more popular.
Assuming you spend roughly about $1000 on a nice suspension setup and have $1500 left to go fast, I'd probably look into either a ported stock heads/intake setup or a GT40 heads & Cobra/5.0 Explorer intake combo, with an off the shelf cam. Properly done, either can produce a 12 second car. Again, you'll need all the correct fuel & airflow parts that we call the 'supporting hardware', and all the 'little things' like bolts and gaskets. Then there's also the cost of shipping, and possibly install costs for some certain things depending on your skill level. Plan ahead, because that stuff can really add up. It's much better to wait a bit longer and make sure you get absolutely everything you'll need ahead of time- It beats tearing your car apart only to realize you're missing something major or the parts you have won't work together.
The best thing you can do is figure out some specific goals and budget ahead of time, and then read up as much as you possibly can. This site is a good resource... try doing searches for whatever topics you want to learn about, it's a good way to find a lot of very helpful information quickly. I'd also think about buying the book 'How to Tune and Modify Your Ford 5.0-Liter Mustang' by Steve Turner- it's a good overall primer on what you can do to these cars, well worth $20 IMO. Sometimes we get so in depth here that I think newbies can be a little confused by all the specifics.
