Eh...I'll answer and explain why the comments.
Your list goes from Harbor Freight knuckle buster crap to Porshe. Sherline to RoboDrill...that is quite a range.
Anyhoo- lets get past that.
If you go the route of Sherline and Shop Bot...I am sure you can make your parts with some finagling...maybe alot. But you will be fighting the machine during the process in achieving desirable results.
Haas is quite a few steps up...the mini-mill would fit...but small work envelope...although you did not offer work size. Problem is...if you find one under 10K...I'd be leery as those machines go for a good deal more...even in poor condition.
Next step up is a VF machine in Haas...same story.
There are Toolroom mills, a CNC Kneemill like a Bridgeport, but not what I'd consider a full CNC as your asking...although several steps up from the Sherline stuff. Again its the low end of Haas...still I'd expect those to go for more then 10K.
RoboDrill- If you can afford one and it fits your needs, buy it. But in your price range of 10K I do not see that as a possibility as they are in a different league. I'd be real skeptical finding one in the 10K range.
That said...you didn't mention tooling, or 4th axis capability or the rotary table, as your going to need to produce your helical gear. Tool holders, tools, vises, clamps, indicators, air compressor...have 3 phase power? If not, you may need to get a phase converter.
Bulletproof- thats like a crash proof car. The bigger more robust they are...the more power they can crash with.
To end this reply...aside from machine budget, figure what tooling and support equipment must be purchased to make parts...could easily go over the cost of your machine. Auctions are great...if you know what your looking at....and even then its is buyer beware. A motor or board on a CNC can put you back several grand not including somebody to diagnose and install.
But ya gotta start someplace. So ask away...