Start with a 7x10 mini-lathe and brass, plus the US Army Field Machining Handbooks. Skip the mini-mill, I own one, but rapidly upgraded to a full size Bridgeport Clone. DRO options are worth their weight in Gold on Mills and Lathes. However I do most of my measuring with a Mitutoyo 500-196-30 Caliper.
View the Mini-Lathe as a kit of parts, they take some hand fitting to get to a .0005" precision over 6" of cut. That took me 48 hours of hand scraping the lathe ways. Do NOT go CNC on your first lathe, you will be endlessly frustrated if you do. Anyone who tells you to begin with CNC while learning the fundamentals of machine tools is doing you a disservice. Little Machine Shop is my preferred vendor for these. You'll need considerable tooling, a rule of thumb is that the tooling/spares/etc. for a machine tool will be at least the same as the cost of the tool when purchased used.
Considering where you live, McMaster Carr corporation is your newest friend....
www.mcmaster.com
Find: US Army, Fundamentals of Machine tools, too big to upload to PL.
US Navy: Machinery Repairman Handbook
US Navy NEETs (electronics self help)
Book: The Art of Electronics, Horrowitz and Hill, Second Edition, NOT the Third.
MIT Machine Shop Videos
Book: Building Scientific Apparatus by Moore and Davis.
Dan Gelbart's videos building prototypes in the shop on Youtube
MrPete222 / Tubal Cain's machining videos on Youtube.
Frank Hoose's mini-lathe.com (<<<<< THIS!)
I can do more quick invention work on the lathe then I do on a Mill daily at the University. The Mill is far more important in the shop, but a beginner can get really, really, creative with a lathe with less chance of ruining the machine and far less expense. Learn on a "disposable" 7x10 or 7x12 with readily replacable parts. Yes, they are junk compared to Bridgeport or Clausing or old South Bend, but a well tuned 7x10 is an utterly amazing piece of junk when working with soft metals such as Aluminum or Brass.
One of the niceties of machine shop tools is you can rapidly destroy your own machine until you learn where to place the cutting head before powering up. Hence my suggestion for a 7x10, replacement parts are cheap.
Avoid Sherline, Taig, Prazi. and lathe/mill combo tools.. Sherline is a good starter for aluminum work, but you will rapidly replace it with a 7x10.
I should warn you, establishing a shop is extremely expensive, and if your proficient with it, well, getting addicted to drugs is probably cheaper.. Makes Aviation with a light sport license look affordable if your not careful. (Not that I would endorse Drugs in any way)
In the lower 48, a good used mill starts at 2,000$ plus another 1000$ in shipping and handling. Not to mention the need for a massive , very dry building, a really solid and level floor, and often three phase power or the need for a 3-7 HP phase converter. Cheap tabletop mills often suffer from deflection issues, even though they look strong, obtaining good results requires massive steel castings in most cases. Hence the full size mill if needed.
In your case it may be easier to send milling out. Used Mills are tricky to buy, and the bugs/wear/old age issues do not show up until you use the machine for a while. I'm not sure I'd ever buy a used one again, but I sure as hell can not afford a new one. :-)
Machine tools are made of a tough steel that rusts nearly instantly if not kept oiled. You can easily ruin your tools by neglecting them.
Evaluate if you have the needed 3D thinking skills on a lathe, you'll know if you have the knack or not really quickly.
abebooks.com is your friend.
You can do some wicked stuff with just a Dremel tool, but that requires thinking and good hand/eye skills.
Please see attached...
Steve