where are you located? that would help to narrow down what your looking for. basically any cnc machine can do what your after but you need to figure tooling, work holding and cam into your budget as well. 60k is alot to start with but lets not get ahead of ourselves. you really need to look at how your going to support yourself when stuff don't sell.
space rental $1000/month
used cnc mill $20k
used cnc lathe $15-20k
tooling up both 10k
really your not up to alot and you haven't made any chips. i'm just letting you know, that your best bet would be to outsource your parts to start and then as you grow invest in machinery. 60k will buy alot of parts. can you turn the 60k into 120k and give yourself a better start? i agree with starting with real machinery. i tried starting my shop with hobby level stuff only to find out that i out grew it very quickly.