Please excuse my ignorance, but is it possible to use a free provider(or system, or whatever it’s called) like Simple Machines Forum, for a forum that is intended to eventually generate income for myself via advertising?
In short, SMF as a software is free always, but as far as server providers go, no - you usually have to choose to either pay for the service or give the possible ad income to the server provider.
Or would I need to ‘rent out’ a forum template (or operating system, or provider, or whatever it’s called) if I have commercial interests? And if I wish to own the rights to my forum, and perhaps even sell it on one day?
You can customize SMF as much as you want, and use it commercially, and hold all the rights to the contents of it - if you don't go for a free provider, and pay for a service that allows you to make working offsite backups of the forum files and database. ( Most paid hosts will, no problem. )
I’m sorry to seem so green, but my own personal work experience is in the NHS in the UK, where if you even so much as *thought* of an invention while you were on NHS time, they immediately owned the rights to that invention. It just seems counterintuitive somehow to get something for nothing - ie the SMF template for a forum, free of charge, and yet own the rights to that forum.
SMF is developed and supported by volunteers, for free, and the software is free to use for any purpose you wish. All we ask is that you support the project by keeping our copyright notices and credits visible, even though you are legally allowed to remove them as well. ( We reserve the right to deny support for forums that remove them however. )
Also, with regard to advertising, is it yourselves that rents out space for ads to generate income, or could I theoretically do so myself if I opened a forum using your template (or system, or whatever)? And if it is the former, does that mean that my only option for making my forum into a business would be to charge users? Personally, I wouldn’t want to charge users because I think there are so many free forums out there that no one would choose to pay to join an unknown new forum.
You can get ads from an advertising network such as Google Adsense, and insert the ads in the forum - or you can rent space directly to advertisers. That is up to you, and there are mods to make this easier.
You can also keep the forum free, and still offer paid memberships that allow access to closed areas of the forum, so it's not necessarily one or the other - you can do both.
Thank you in advance for any advice 
You're welcome.
https://wiki.simplemachines.org/smf/InstallingIf you come up with other questions, please feel free to ask.
