As a relatively new machinist, (only in the last year).
I would recommend buying the best lathe with upgrades, and mill with upgrades that you can afford. Power cross feed ect.
There are other essentials which I think have been posted above already but what I have found most needed is the basics.
A bench mounted grinder, HSS tooling blanks that can be ground to shape, a wet stone to round off the tip, (a greater radius means a smoother finish), a magnetic base and a Dial test indicator, veniers, and micrometers from 0-1", 1-2". Plus a good set of HSS drills. Make sure that you get a four jaw chuck as this will hold any shape material, and can be centered easily.
For the mill an ER collet holder and a small selection of collets, 1/4", 3/8", and 1/2", and end mills to suit, a vise and a clamping set. I can't really comment too much on the mill as i dont have one yet, but one is coming soon.
Anything else can be bought as the need arises, but that is what is consider a beginners set. And most of what I've said above I found out very early that I needed.
Edited By Jon Cameron on 04/02/2018 14:05:03