I REALLY like 12L14 for short-n-sweet projects. Yup. It rusts. <shrug> Blue it, oil it, keep it forever!
I prefer drill rod of about any flavor, over crappy old 1018. 1018 is just misery, unless you got your lips held just right, and you guessed the right color chicken to bury under the oak tree, etc.
Rifle barrel steel is formulated to be pretty decent to machine. Talk nice to your gun-plumber, and you might be able to scrounge some up. It already has a hole down the middle! (more or less)
17-4PH steel is nice stuff. It's a stainless that hardens by being cooked in the oven (precipitation hardening, the PH in it's name) and, while it behaves a bit differently than mild steel, it turns to a smooth finish, really easily. Expensive if you are buying lots, but worth looking for in the offcuts bin at places that have the stuff, like Metals Supermarket.
Carbide tooling is expensive, and the frustration factor can be really high when learning to use it, as the edges break really easy if bumped or mistreated. HSS tool blanks are cheap and easy to grind, and are pretty forgiving.
Once you learn to grind a decent cutting tool, you will find that the HSS tools can be made to do just about anything you need them to, on a lathe.
Cheers
Trev