Unlike most people here, I would recommend a mill. It's just such a versatile machine. On our lathe we make spacers and the occasional round part, and on our mill, we make everything else. Get a good one with a digital readout, and you can make an amazing range of parts. If you are at all interested making gearboxes and custom drive trains, a milling machine is indispensable. We are fortunate enough to have both machines, and our milling machine gets *way* more use. This might be because I am much more experienced on a mill and I encourage it's use
But we also encourage the students to work from drawings, and the digital readout on the mill really helps make the connection between the dimensions on the drawing and the dimensions of the part they are making. Our lathe currently only has dials to go by, so it it a lot less user friendly. I guess whether you decide to go with a lathe or a mill, I would recommend spending the extra to get one with a digital readout, and the machine will be much easier to use.
Rob