I'd go 13" minimum. A larger lathe will use a larger chuck, which means a larger center hole to grab larger workpieces without having them stick way out & be unstable.
You can get more bang for your buck going with used equipment as long as it isn't worn out. There are small machinery dealers who buy out closing shops & sell off the equipment. Don't forget to budget money for tooling. I bought an off brand tool grinder which really helps sharpen to the correct angle. I use a quick change Aloris tool post. I have a 15" lathe & it does 99% of what I need done.
Here's a website with equipment.
http://www.machinetools.com/us