Howdy Back Nick:
Here's an idea. Take a look on the driver's side door jam for a build plate. It will give codes for "Axle". If you will post it someone will look up the axle ratio for you. If it is a number is is an open rearend. If it is a letter it is an Equa-Lock differential. The stock '66 7.25" rear is quite tough. They seldom break all at once. They just start to howl, leak and get loose. (Hey, that sounds like me) and gradually decline. Parts are available but scarce. If you have to rebuild, an 8" from an early 70 Maverick/Comet is a better choice.
If you do go to a T5 as your first upgrade you will not mind the typical, low ratio as much because of the overdrive 5th gear. And you are right about your engine feeling stronger as you are able to keep it in its power band better.
A five lug axle does allow more choices in wheels, but there are other limiting factors as well. Changing the rear axle is not too difficult, changing the front hubs to 5 lug is more of a committment. There are better ways to spend your time and money, in my opinion. Please do heed those who suggested you spend some time and money on making your brakes and suspension safe.
It would be good if you had a plan, or vision of what you want to have when you finish, how much you want to spend, and how you want to enjoy this car. I always like to start with the free or cheap and easy upgrades, get a plan and then prioritize.
The T5 upgrade is a relatively expensive and complicated one, but one of the most satisfying for folks who like to drive their babies.
Your choice.
Adios, David