I'd suggest cheap cutting tools to start with. HSS won't always cut what I have to cut so I also use the cheap HF carbide. While they might not cut good they still cut & I don't feel as bad burning up or breaking a $1 bit as a $3 one. If you use Android there are some apps out there with great information. I use them to get spindle speed mostly. I'd suggest thinking up a simple project & figure which tools you want to use to approach it. You might make your first project to make a tool you will use later. I used a cheap Drill press vice from HF until last month. It was what I could afford at the time. So my first project was to turn two pieces of round rod that was hard enough not to give(home made parallels) so I could lay them on my table & pull the vice down to them to mill the bottom of the vice to be parallel to the rails of the vice then bolted out down on the table right & indicated it as close as I could & started machining all the other aspects of it.
Some tools will be moved from one machine to the other.
I'd suggest minimum tooling for the lathe: to be HSS tool blank or preground to get started turning first, carbide only if you need it for hard stuff, drills, & center drill.
For the mill: set of 2 flute HSS up to 1/2", collets, 1/8"-1" in 1/16", drill chuck, fly cutter, parallels, rubber mallet, clamping bars w/risers, & a vise if you can swing it.
Measuring: a indicater as precise as you need to be, pin gauges, micrometers, digital caliper, blue sharpy, & a way of mounting the indicater.
Stuff that might be a must for you depending on the job or you don't already have it: common hand tools (the Asian machines come with most that you will need), bench grinder (I use a belt sander more but still need the grinder), boring head w/bars, (believe it or not)super glue, a tool to correct concentric(this is another good learning project, I milled a square shaft to fit my tool holder & turned the end down to press a roller skate bearing on), & probably a saw to cut stock.
How much money do you have I can spend for you?