You can break up the exhaust into three main components: Headers, Mid Pipe, and Cat-back.
Headers bolt right onto the engine, it's where the exhaust system starts. You have some of your own options here. IMO the worst you can do would be "equal length 'shorty' (short length) headers". Theoretically these are the opposite of what you want to do since you really want unobstructed airflow. Than you have plain ole' "Shorty" headers which is a slight improvement but again theoretically since each exhaust port/tube is unequal it doesn't provide the best airflow. The best, for performance and aesthetics (e.g. sound) would be Long Tube (LT) headers. Each exhaust is cut and bent to provide equal length for each port before the exhaust combines into one and goes through the rest of the exhaust.
If you decide to go with LT headers and you keep your O2 sensors (discussed in a bit) you will also need an O2 extension harness since the O2 sensors will be moved further from where they currently are.
Again there are many options for Mid Pipes. The first thing you will want to decide is if you want to stay "legal" or not, so to speak. This meaning if you want to keep your Catalytic Converters (Cats) or go "off-road" (no Cats). Some brands also offer "Hi Flow-" or "Racing Cats" which is a way to pass emissions while still getting a few more HP out through the Cats.
After you figure that out you can figure out how you want them set up, i.e., more options. You have H-pipe, which I believe is how the stock exhaust comes, but the aftermarket is a much better set up. The H-pipe sounds great on the V8 and gives the exhaust a nice low grumble sound. You then have an X-pipe which is similar but the exhaust crosses more like an "X" rather than the "H". X-pipes tend to give the exhaust a bit of a raspy tone, but still makes the exhaust sound nice. Performance gains are about the same for either the H- or X-pipe. Then you also have the Pro-Chamber. The Pro-Chamber is basically a small chamber where the exhaust pipes meet after the headers and before they split again to the rest of the exhaust. Pro-Chambers also have a nice sound to them and are supposed to give a few more performance gains over the H- or X-pipe. One other option is just to have two individual pipes welded in to have "true dual" exhaust or rather two separate pipes for the exhaust.
You should pair your Headers along with your Mid Pipe as certain manufacturers' will not match up correctly.
Mid-pipes also have your O2 sensors (Oxygen sensors). Deleting your Cats will cause your car's ECU/PCM (computer) to think the Cats are not doing there jobs and cause a check engine
light (CEL; Service Engine Soon (SES); Malfunctioning Indicator Lamp (MIL)). You can pick up a hand held tuner or go to a shop that can tune cars and they can remove the CEL for you. You can also purchase MIL Eliminators which plug right in line with the O2 sensors. Of course there are plenty of sites that will show you how to make your own MIL eliminators from parts you can get at Radio Shack.
Cat-backs are pretty much universal, even to the stock Mustang's exhaust, you can get a cat-back exhaust and bolt it right up. Cat-back is short for "Catalytic and back" and bolts up right to the factory Cats, or Mid Pipe and includes the mufflers and exhaust tips.
Each manufacturer has their own sound and claims of performance.
Now there are still a few other options. You can shorten the cat-back to axle-back (although I think that's more common, or only for for the S197 ('05+) body style) which bolts up behind the car's rear axle and ends at the car's exhaust tips. A cheaper option would to just get new Mufflers which would give you more sound but minimal increase in performance. Exhaust tips are purely visual aesthetic.
Finally, as far as exhaust options go, you can just go to a muffler and welding shop and get some pipes welded in, anyway you want. Go with true duals, or an X-pipe, or Figure 8's if you really want (which come to think of it would be interesting). Custom headers made even, or just some pieces to replace the stock, or from the headers to the exhaust tips.
The more exhaust you can get, the more overall performance and sound you can gain and "control" meaning to get the sound you are looking for.
The best way to find a sound you like is YouTube. Search for exhaust clips and see what you like and don't like. You may already have an idea of what you want your car to sound like so you can also start from there.
As for Manufacturers, that is another preference and recommendations. If you want we can sit here and list what's good and what's bad for this reason or that reason, but ultimately it's your car and it's what you want to have.