A lathe can be used to mill stuff, a mill can be used to turn stuff, neither is as good as having the correct machines.
If you have to start somewhere, though, get a lathe. There is a LOT more flexibility available to you with a lathe in the shop as your only machine tool than having only a mill.
That said, you could be one of the guys that needs a mill to make what he wants to make.
On the presumption that you ARE just starting out, what have you in the way of reference material?
I'll suggest a couple that are available from Busy Bee. The Amateur's Lathe by Sparey, Work Holding in the Lathe, and Milling in the Lathe by Tubal Cain (the pen name of a Brit by the name of T.D. Walshaw), and find an older edition of Technology of Machine Tools, by Krar. The first is an all round good book on lathe use, well written and readable, the latter two are chock full of ideas that will come in handy, and will give you a much better idea of how to solve some really difficult workholding problems.
Technology of Machine tools is a standard High School/College Metalworking shop text You don't need the newest edition for $80 or more. Look for about the $20 range! The information you will get is timeless, and the changes to the newer editions are mostly about CNC.
South Bend's book How to Run a Lathe is available inexpensively as reprints too, or you can hunt around and download a copy.
If you are at all nervous about spending the money on books, borrow them through your public library first to 'screen' them.
Cheers
Trev