You probably want a open ratio (2.78 1st as opposed to the closed ratio 2.32 1st) Toploader with the small input/output shaft. Some closed ratio trannys had small in/out behind 390's and they'll work, just the 1st gear is different.
A toploader is called that because there is a top plate that the gears go into, the case doesn't split open to service. Your 3 speed is a top loader. Some Mustangs also came with a T-10 4-speed which will also work, but by most, is less desirable. A toploader is stronger, the Jerico tranny is designed from the toploader.
The numbers or codes are only needed if your trying to "match" the tranny to the year of the car, but since your car came with a 3-speed, its probably not that big of a deal. The only thing your looking for is the right length tailshaft housing.
Your bellhousing will work, if memory serves, all you need is the tranny and a shifter with its linkage. If the 3-speed bellhousing won't work, Ebay has cast iron ones cheap, or you can get a Lakewood off ebay pretty cheap.
All 4-speeds are not toploaders, the T-10 isn't. Also, not all toploaders are 4-speeds. Your 3-speed is one, but a late model 3+1 looks like a 4-speed but is really a 3-speed with an overdrive. This is where understanding part numbers comes in. The tranny you want will probably start with a D3 or earlier ('73). These 3+1 are also recognixed by a bump on the front passenger side that helps to differentiate them.
If you get the right tranny, you shouldn't have to modify the drive shaft or anything. It just bolts in.
I took the 3-speed out of my '65 coupe and put in a 4-speed from a Boss 351. I had the shifter, linkage, tranny and bellhousing. I used my clutch, pressure plate, clutch fork and throw-out bearing, and the yoke that was on the front of the driveshaft that was in my car. The Boss cars came with a Hurst Shifter, so my 3-speed boot didn't work, but most parts stores have these on the shelf. Even the Speedo cable went into the tranny.
