3rd gear in your 3-speed is straight through, same as 4th in a 4-speed (most of them) so, if you are going to change the tranny, you need to go with one that has an overdrive.
Yes, you can change out the rear end (or just ring and pinion if you can find one to fit). Depending on how much faster you want to go, 3.73 may get you there.
Taller tires may also fit and get you a bit more speed (how much more speed depends on how tall).
You can also look at a Ranger overdrive unit. They go in front of your transmission, between the bellhousing and tranny, that is probably a lot more than swapping out the rear end though.
