What does it mean for a menu to be a "set menu"? I hope this question isn't too off topic. What does it mean for a restaurant to have a "set menu"? The one I have in mine has three headings wit the descriptions: "starters...assortment as brought to the table to share family style"; "mains...each guest will chose their own"; "desert"...assortment as brought to the table to share family style". How does this work? I'm guessing it means you choose one from each category, and no matter your selection the price is the same? What does the part about family style or choose your own mean?
Collins dictionary gives a nice definition for a set menu:


  A complete meal in a restaurant or café for a stated price with a limited number of options to choose from for each course [...]


The different serving options are 


family style:
Like you would probably serve food at the family dinner table: every component in its own serving bowl or platter, to be passed round amongst the diners. In a restaurant, often a nice platter of various dishes to be shared.
individually plated:
This is what you are probably expect first when dining in a restaurant - each diner gets his or her choosen dish on his or her own plate. 


So for your case: 
For n diners you build a menu out of n appetizers or starters that get served on one (or a few) platter(s) and is then shared. Of course you can choose n different options or stick to larger quantities of fewer choices.
The main dish comes on n individual plates according to each participant's order and the dessert is again n servings of whatever you pick, like for starters.

And yes, if that is described a set menu, you'll pay a fixed price per person, unless some options are marked with an extra charge, but that would have to be stated clearly on the menu.

You can of course build a menu à la carte instead, then you pick the individual dishes from the à la carte menu - these have individual prices that make up the total cost of the meal.