Re: New here - etiquette question!
There are actually a lot of 'private' games on here. I was first introduced to the site by a friend who wanted to use it to run a Star Wars game for several of us who'd been scattered around through the years.
I'm currently in a couple of games that, while populated by RPOL 'regulars', are technically private...in that, the pool of players were all invited to join the game, either by the GM or by players the GM trusted to invite someone.
So, no, it's not a faux pas, and not even necessarily that uncommon.
As for the question of using Groups, or making it Adult...even if you just run it as a common game, the most anyone can do is read. They can't get into the game without your approval...so unless you're concerned about maintaining some privacy factor (why, I have no idea, but some people are funny about strangers reading over their virtual shoulder), you can just run it like any other game. If you don't set the flag for it, nobody is going to think you're adding players (and you still can, even without the flag set). If you don't advertise on the Wanted: Players forum, odds are good that most RPOLers won't ever even know your game exists. You can contact the people you want to include, tell them the game to search for, and they can click on the link and Request Access (so could anyone else who stumbles on it...but until you approve them, they're not part of the game.)