Can't help you with Proxxon or Toyo (don't they make tyres?), as I've never seen either. Sherline tools absolutely do not need to be rebuilt- they are ready to run out of the box. Of course you can rebuild them whenever you want, but they don't need to be 'cleaned up' like many generic machines. They have a backlash of about 0.002"- but it's not the same as play.
I've never dealt with a dealer- there just isn't one in my part of the world. I can understand you're wanting to have one close by (and envy those that have access to one), but it hasn't slowed me.
Machinery's Handbook is the bible of the machining industry. It could probably be compared to a graduate level text. Useful but likely overkill for a hobbyist. A separate guide is even published on how to use it.
A less comprehensive but more practical introduction might be
Tabletop Machining. It was written by the president of Sherline, so it certainly has a Sherline bias. But the info in it is inherently useful on all small (and most large) machines.