Will, i got the first half of that, you kinda lost me in the second half...
Well, I can't know your skills but I'm going to assume you haven't done a lot of towing. Maybe you are a truck driver for all I know.
Jump up and down on the rear bumper of your Ranger. That's what you are going to hook a 4,500# trailer to. A Ranger is meant to drive smoothly and the springs are variable rate meaning until you get a load on it they are quite soft. An equalizer hitch is going to try to close the bottom of the truck and trailer together like a jack knife. So if you go with 450# of tongue weight, you only want to unload the hitch point by 100# when you crank the equalizer bars down. That's going to be hard to calculate since I am assuming you are going to pick something up and won't have a lot of means to adjust things. It could be worse to have the equalizer than to not have it. You really need to be able to mock this up at home and try it out first.
The other thing I was talking about was that the rear end of a Ranger is pretty light--maybe 1,400#. You will maybe bring it close to 2,000# with the trailer. The trailer, being much heavier, has a decent chance of pushing the rear end of the truck around in certain circumstances. A turn on sandy or wet pavement, for instance.
A bigger truck is always better, of course. But I think you can safely manage.
As to the auto VS manual, I prefer the auto. I think it's physically stronger and is defiantely better from a stop. Ford doesn't give the Ranger manual a very good first gear. You should never apply power to a slipping clutch but with a 3.40 first gear and 10,000 load you don't have much choice. Just get it up as quickly as you can and once you are rolling take the rpms all the way up to redline before each shift and then let the clutch up fully before accelerating in the next gear.
The auto has the torque converter which doubles the torque under maximum load. From a stop at full throttle it's like having a 5-1 first gear. Once you are cruising the converter clutch locks up and there really isn't a mileage difference. On hills the converter will unlock and split gears--and make a lot of heat doing it. You would, either with a manual or auto, downshift and let the engine spin on grades. The auto is also actively cooled and the manual is not.