In some cultures, 16 (or 15) is a big deal with a huge celebration. I don't know if that's the case with you, your cultural background, and your overseas relatives. But it's not always the case in the US. I don't know one 16 year old who had a big venue with a DJ! My son is in his 20s, and he never went to a party like you describe, and never heard of one either. Not one!
I think you have a good instinct here, that it would be a bad idea to invite dozens of kids you don't know well, and then have them not show up. In the US, a lot of huge parties (whether they are for 3 year olds, 8 year olds, or 16 year olds) start to look like an excuse to collect a lot of birthday gifts! And you really don't want that to be the impression you give by inviting kids you don't know well!
It's nice that your mom wants to give you a big celebration, but it does sound a lot like this party is for HER (or for her to "prove" that she's a good and devoted mother) than it is a reflection of your social circle. If you give a party, you send out specific invitations and request specific RSVPs, and that's how you have a head count. But the problem with teen parties is that sometimes the word "gets out" and then friends of the people who are invited decide to show up. And it gets out of control because you don't know half of the people there and your mom won't be able to regulate it.
I'd sit your mom down and say, "Look, this isn't what I want. And it's a huge risk because you would be spending a fortune on people you don't know, and you'd have to police them to be sure no one brings in alcohol. That's a legal liability, Mom. I don't want to invite people I'm not friendly with, I don't want to look ridiculous, and I don't want to look like I'm out to get presents. Please respect me in this."
Then I'd suggest something you WOULD like. Can you think of one (or 2) friends whom you enjoy, and then think of something you might like to do? Perhaps a movie for just you and a friend (with or without your mom and sister)? Look and see what's playing in the theater, and maybe go to dinner before or afterwards at a casual place whose food you like. Or consider finding something on TV (Netflix, On Demand) or even renting a classic DVD from the library. Make your own pizzas, make some popcorn, and watch the movie. Or come up with a craft you would enjoy. Is there a local museum with an interesting exhibit? A restaurant with a trivia night (you can listen in even if you don't compete). A comedy club that is appropriate for teens? Some historical landmark that has interesting programs? (In Boston, for example, we have The Freedom Trail and Duck Boat tours.) How about an afternoon kayaking or canoeing, if you like that. What about those "Escape Room" events where a group of people has to cooperate to solve a problem and get out of the room (they come get you after an hour if you haven't figured it out! Not to worry!) Some groups I've seen do an urban "scavenger hunt" where a series of clues leads you to the next stop - just a fun team-building exercise that people use for special birthdays, bridesmaids fun, and more. These can be done with 3-4 people, which might be you, your mom, your sister and one friend.
Set a budget with your mother, and be sure that the chosen activities reflect YOU and what you would enjoy. It's okay to stretch beyond your comfort zone just a little, but not so far that you will be miserable or anxious! After all, this is YOUR birthday!
