1 1/2 HP might be a bit big for that lathe, 1 HP should be more than enough. If I remember correctly, 3/4 HP was the recommended motor for that lathe. I had one just like it a long long time ago. Take a look at the Frame Size on your existing motor, it should be a 56 or maybe a 182. Match the same frame size in a single phase motor and the pulley will fit.
As far as motor go, Dayton, Baldor, Iron Horse are all good brands. Make sure what ever you get is reversible. Another option is to put a VFD on your existing motor. pretty inexpensive way to go.