One factor that hasn't been brought up yet is power transfer ability. You say the motor is rated 2.5 hp. You simply cannot transfer unlimited power between two shafts with just any belt and any pulley diameters. It's all about the grip area, and very controlled slippage. It's a given that the sides of the belt must slide (or slip) up the walls of the pulley (if you are using a vee belt anyway) as it exits the pulley. But you must have enough surface contact between the belt drive/driven surfaces, in the case of vee belts the flanks, to transfer the power to and from the pulleys. Imagine, as an exercise, how much power it would take to make a belt slip on a 3 foot diameter pulley versus a 1/2" pulley. Enormous difference in the gripping surface area. Ignoring the flex around the 1/2" pulley, which one would slip first? Of course it would be the smaller of the two.
Now in your case, what kind of belting are you going to use? A flat belt, or a serpentine belt has other limiting factors, but let's just talk about vee belts. I haven't looked it up, but will a typical a section or b section vee belt handle 2.5 hp on a 1 1/8" pulley? I doubt it would be even recommended to bend an a or b belt that tight, so you have another problem with belt selection. Of course, the lathe pulley is already there and let's assume it's fixed and you will not change it. Probably true anyway. Would be in my case. So there is a sizable dilemma in itself. I believe you need additional information on belt drive apparatus before you select the pulley.
The speed ranges you have are about right. I would go for the middle I think, aside from all that above. Even then, the back gears only will give you around 60 RPM for the lowest speed though. If you're OK threading and knurling at those speeds, then it's fine. Lots of lathes turn slower though. Just your own comfort level.