Hi, and welcome to Hobby Machinist forum... I think you will find lots of friendly folks here who will listen and suggest things.
I came to this forum in early July... I was at a similar place to you... albeit the machining goals were different.
I fiddle with and fly EAB aircraft (think barnstormers... LOL), as well as making non-aviation related custom parts for folks.
I started with a desire for a PM1127 and a PM25 (well, the preceding mill to the PM25... Matt improved the product, it is now called the 25). Then after a lot of study... decided to upgrade to a PM932/PDF (a nicer version of a PM45). Then decided to upgrade to a 1236 lathe. This kinda fit my budget... until I got to looking at the machines in person (local folks)... First I bit the bullet and upgraded to the 1340GT lathe... then after a few weeks of indecision upgraded to the PM935TS mill. Both of these are Taiwanese made machines, the quality is a HUGE step up.
IMO these three combinations are good groups:
1127 and 25
1236 and 45/932
1340GT and 935TS/TV
Depending on whether your needs are mill or lathe intensive... might mix and match.
From someone that has studied this for close to 4 months...
Your budget may be a little soft...
With around $10K:
You can get the 1127/25 with lots of tooling
You can get the 1236/45-932 with a little tooling
Or you cannot get the 1340/935 for even more than your budget with no tooling
Now lets talk a little about machine size: The reason a machine tool is massive and heavy is something called chatter.
The operation of cutting metal is in reality somewhere between chiseling and scraping... precisely controlled gouging might be a sloppy way to invision it. The more DOC (depth of cut) one takes, the more the tool tends to want to vibrate (or chatter). Now cast iron is really good at absorbing that chatter, so it does not result in a wavy and rough finish of the cut.
The little machines will take little cuts, but chatter with larger cuts.
The middle machines will offer some more strength while taking deeper cuts
The Taiwanese pair noted above, will take a little more DOC, yet do it with more precision... and they are just built to tighter standards. Note the 1340GT G=gunsmithing, T=Taiwanese
While we are talking about precision and accuracy: Something to understand: The ability to make a precision part (hold tight tolerances) is as much--if not more--the operator... than the machine... and this takes lots of time to learn.
However a well made and well maintained machine helps.
If it were me... given your list of things you want to do...
I would look seriously at the 1236/45-932 (with the PDF feature)... and figure on spending more as you need specific tooling.
You can start off with not a lot of tooling (you will need measuring tools and basic cutting tools)... then add things (rotary table) as you need them.
BTW: Amazon has lots of stuff, and it is relatively competitive (not machines, tooling). Get a Prime account... freight is free.
Here is a thought: You can always get more tooling... however it is hard to get more machine without upgrading...
And here is something to consider: QUALITY!
Matt's PrecisionMatthews machines are subtly a cut above... little details which become quite noticeable if they are missing. And Matt is a wonderful guy to work with. If it were me, I would not let flashy deals get my attention... one usually gets what they pay for... regardless of the fluff.
Hope all this helps, please feel free to ask all the questions you want... someone will do their best to answer them.