Your best option, in my opinion, is to look up what axle ratio you have now and then buy the whole axle assembly from a wrecking yard
On back edge of drivers door is your build label
Under AXLE will be a 2 digit code, then look it up here:
https://www.therangerstation.com/tech_library/axle_codes.shtml
You can use either a 7.5'' or 8.8" axle, they both bolt in the same way and use the same drive shaft
Upgrading to a L/S(limited slip) would be a nice upgrade, again no external changes needed OPEN or L/S just bolt in
Contrary to what's happened to yours, the 7.5" and 8.8" Ranger axles is a pretty safe buy used
car-part.com is a good place to search your area
Looking for "rear axle assy(RWD)"
1993 to 2009 7.5" or 8.8" rear axle assembly from a Ranger or Mazda B-series, will work your 2001 Ranger
Obviously, later years should have lower miles on them
You can use 9" or 10" brakes
Look at your rear brake drums, if you see fins then they are 9", if the drums are smooth on the outside then they are 10"