Looking at your car I assume it's a '99-'04 GT. Differentiating between a V6 and V8 is a big deal because the V6 stangs use a 7.5" rear end and it's bigger brother the V8 GTs use a 8.8" rear. There's nothing wrong with either rear-end but parts will be application specific so be wary when you choose and don't be afraid to ask questions, both on this forum and at the shop you choose to do an install. Also; BIG THING: Shop around on install prices. Most shops wanted to charge me $550+ just for install but I finally found a decent shop to charge me only $373 after tax for install and 6 month warranty(in case of whine or malfunction).
I'm linking you to a 8.8 rear-end specific parts for mustangs ranging from years 1999 to 2004. Again note your year when selecting.
Here is the link for the actual gear(I'm linking you to 4.10 set because it's my favorite. If you want 3.73 search for it yourself haha). The different manufactures that are popular are Motive, Richmond, FRPP, and a couple others.. I always choose FRPP because I've heard mixed reviews about all other gear sets but only good about FRPP:
Ford Racing 4.10 Gears (99-04 GT) M-4209-G410A
Here is the link for the T-LOK rebuild kit for 8.8s. It's highly recommended since you're already gonna have a shop open it up to get this rebuilt on higher mileage vehicles(or vehicles that get driven hard). That being said.. I didn't do this when I installed my gears at 105K miles in my GT and haven't had any problems. It's your choice but highly recommended:
Ford Racing 8.8" Traction-LOK Rebuild Kit w/ Carbon Discs M-4700-C
Here is the install kit which a shop will need to complete install. I linked you to the install kit with the bearing rebuild because, like the T-LOK rebuild, it's nice to do it while it's apart and be done with it; especially for higher mileage vehicles. It's cheap, too. The install only kit is like $35 so why not step up while here? I did choose this option:
Rear End Installation and Bearing Kit (8.8in) R8.8RMK
And finally here is the gear oil. I think it takes 3 bottles but I bought 4. You don't HAVE to use royal purple but it has a pretty great rep for what it does. Just make sure to read up on whatever oil you do choose. A 8.8 GT takes 75w90 gear oil:
Royal Purple Max Gear 75w90 Mustang Gear Oil 1300
Good luck and don't fear the gear. Like I said I went 4.10 and am extremely happy with it. Read the threads in my signature for a bit more information, discussion, and experiences with 4.10s.
Edit: To answer an earlier question about "what is considered high mileage"; It's all relative. It really depends on the age and condition of the vehicle. Like if I had a 1989 GT and went to swap gears I'd do a complete rebuild, I don't care if it had 10k miles on it. That being said, my 2002 GT had 105k miles when I did the gear swap and I rebuilt everything except TLOK. For $100 bucks it's a great peace of mind thing but I felt the car was still relatively underpowered to really cause any problems on a 105k mile TLOK and I don't ride it that hard so I wasn't worried. Generally I'd say rebuild the whole thing if it's pre-'95 no matter the miles. And after '95 I'd say over 100k miles recommended total rebuild, definitely bearings at least. And over 130kmiles any year should go ahead and rebuild. I'm no mechanic but I've read up a lot on it and been there done that... It's just peace of mind, like I said, and what I'd suggest and what I've heard suggested.