To avoid becoming a TLDR:
In short, watch the MIT Machine Shop video series on YouTube and invest in a brand new, high-quality, almost too big for a benchtop milling machine.
In long, reasoning continued below.
I came from a similar background and have recently (~1 year ago) taken the same leap you are describing. I also had a welder and various saws when it came down to a lathe or a mill. It will depend on your personal use.
I build liquid rocket engines primarily so going with the lathe was a given. It is also the machine that I have the most experience with.
There were a few things that I overlooked when I transitioned careers from a race team that had a fully equipped machine shop to my current position at Cape Canaveral where I'm not allowed to use the machine shop. Simple things like a perfectly flat granite bench, numerous parallels, indicators, references in general are a lot harder to come by in my then spare bedroom, now rocket research lab. When you are working within any kind of critical tolerances references are more important that the cuts most of the time. I also didn't realize that I had to rebuild my testing entire infrastructure including my thrust stand, plumbing, electrical connections, sensors... etc before I would even get to building a rocket.
Sorry for thinking out loud but I wish I had said all of these things to myself before my purchase. I do not regret my decision. I love my lathe like a child but I would have gone with a mill because of self-contained reference/indexability and its versatility. What you can do on a lathe you can do on a mill (rotary table/boring head) and visa-versa but a mill will give you a more expanded capacity at the sacrifice of speed when working with round/turnable parts. In the end, you can always build yourself a lathe with a mill!
When it comes to sizing a lathe or a mill, it again depends on your conditions but the critical size seems to be about 7x14" for a lathe and maybe 9x21" for a mill table which I would consider the upper end of the "mini" machine category. If you are dealing in this regime, it will be wise to go with a new machine and just invest the money. Increased prices here do account for quality still until you get to pricing for more features which should be in the range of $700-$1300.
After that or if your desire more capacity, its probably a better choice to try and craigslist a well used higher quaility full sized machine like an atlas or a bridgeport. Emphasis on the well used, not "like new" because more than likely someone with the money to buy a new machine that barely gets used or broken in, either didn't or doesn't know how to maintain it and use it properly. When buying used, reference YouTube University to learn what to look for and always ask the previous owner about any qwerks because every machine develops a personality of its own. If you are going to be working on gearhead type projects primarily than the mini machines should certainly be able to cover most of what you would need.
No matter what you choose you (and anyone who has ever held a wrench) should definitely watch the MIT Machine Shop video series on youtube. I have a couple thousand hours into machining on everything from 7hp lathes to Cincinnati Mills to my current 7x Grizzly lathe and Tormak CNC machines and everytime I watch the series or have it playing in the background I learn something new. In terms of learning curves, I feel like a mill spinning a 1/8 inch bit is a lot more forgiving than a lathe spinning a 1 foot chunk of 6 in round a few thousand rpms imo.
I hope that there is something of significance lost somewhere in that ramble. Let me know if I can help you out in any other way.