Question about Multiplayer servers/setup

I'm working on a space sim shooter with offline for practice and online competitive multiplayer (16v16, 24v24, and 32v32)

I'm in unfamiliar grounds when it comes to the multiplayer aspect so not really sure the best setup or configuration. I was thinking a server for login/patching, etc. and a separate server for the game (or more depending on player count). Also I want to reduce the cheating/hacking so I know I want to have an authoritative server but my questions are:

1) Is there a service available that offers low overhead (to keep good performance)

2) Or would it be better to purchase my own dedicated server

3) Realistically how many players would/should each option hold?

Any good tutorial on how to setup a server for your game? (besides read the api docs answers please)

Thanks