You didn't say what size lathe you're looking for so how about a Chinese mini lathe? It was my first machine and despite having a big lathe and a mill I sometimes come back to the mini lathe when I'm making small/very precise stuff. Also starting with a mini lathe is good from safety point of view. It's not going to rip your arm out if you make beginner mistakes.
There are many versions of this machine. I suggest to get one advertised as "all metal gears" and with an rpm display.
There are many versions of this machine. I suggest to get one advertised as "all metal gears" and with an rpm display.