You've "only" got a $50k budget and your looking at machines that ornerynorsk correctly referred to as a toy? Defo check out the dedicated machine tool auction sites for second hand. If limited on space Haas and I believe others produce mini mills that would meet your requirements.
So What do I do?
I've got the opportunity to set up on my own after 15 years in the game. I've been offered some workshop space, but the door into the workshop is ridiculously small. 1.85m!! (its an old forge). However if I removed the shutter doors (about a days work) I can gain an extra...