Really depends on what you plan to do with it. Square or round type of person. I drilled and needed to size/cut down flat/rectangular materials to specific shapes, so the bench mill was first. Having never had either nor any tool specific schooling on their use, I think that changes your prospective a bit. I also built boats in my younger years, so had more of a woodworking/table saw (sizing material) and drill press mentality. I could make things round if needed on the mill, and used it for several years first, built lots of parts and improvised. The lathe came several years later, and all self taught. The lathe allowed a whole new avenue of part making, but for me, I do more on the mill (but really enjoy making parts on the lathe). Both just as important, just different avenues on what you plan to use it for. I would look at it more from the point of view, you need both, how do you want to divide up the money, and where are you going to put them. I found the mill more innate and easier to use up front, the lathe took longer to learn all the aspects. In the end the lathe cost quite a bit more than the mill, and the tooling was significantly more than tooling for the mill. So if you start out with a limited pot of change, look at the total costs, not just the machine itself.
Maybe when teaching machining they start out on the mill, because in theory the risk and the damage to the machine is less if you mess up. I am careful using the mill, and extra careful with the lathe. The other essential item that I finally purchased was a metal band saw. Use to take me hours cutting stock by hand (or jigsaw), now 20-30 seconds and it is done. Probably need to learn some welding next, just to know how to do it. I have no space for anymore equipment.