Once you have the names of various tournament formats, then it is easy to research details yourself until you find one you like. One advantage of having a friendly (unrated) local tournament is that you can decide on which format may work best for your group.
The online tournaments with a timer that you are referring to are probably "Arena" format. However, given your situation with around 15 casual players: I'd recommend "Swiss" format. The positive with Swiss-events is that players who win more get paired with players who are doing just as well. "Round Robin" format might also be a decent option for 15 or so players, but again it depends on what you want and what makes sense for your group.
https://en.wikipedia.org/wiki/Swiss-system_tournament
https://en.wikipedia.org/wiki/Round-robin_tournament
This should serve as a springboard for your research into which style of tournament you choose. Let me know which format you decide on and how the event goes; I might be in your position someday. 
Hi All,
Not sure if this is the right forum catagory, but I was looking for some help with setting up a local chess tournament format with 14-15 players.
At the moment, I've just put all names into a bracket-style elimination tournament generator template. Where the winner of each pair goes on to play the winner of the next pair, and so on until a final winner is established.
But are there better formats that allow players to play more than the assigned opponent they have at the start?
When I play some tournaments on here, it's like an overall countdown timer, and I'm not sure how the rankings work ,but after each game, you re-game against someone else, and I think the winner at the end has the best wins, loss, draw ratio? Not sure.
Any blue-prints to mapping out a basic chess tournament for 14-15 casual players would be greatly appreciated!