My daughter just turned 13 as well. We had a girls only party though. If you get too many people you are going to have to have extra adults to help keep eyes on them. It's a great age, but some are more grown than others and will attempt whatever they think they can get away with. When you add boys that opens up a whole other set of doors that you are going to have to watch. Vice Versa ( I don't want it to seem like I am picking on the boys, I have 2 of them also).
With our oldest son we had a pool party and even still 3 of them sneaked off with each other, after saying they were going home and were going to wait for their parents out front. Parents showed up and kids weren't out front. We found them they were around the corner, but gave us a scare. So, I would say like 1 adult for every 4 -5 teens.
The pool party however, is the best way to keep them all in the same place and busy and not break the bank. The other party ideas are awesome, just when you get that age range together and mix it with boys and girls they aren't interested in the same stuff and they don't want to look uncool in front of the opposite sex.
You have the pool party, have pizza's delivered, have an ice chest full of soda's, a table set up with chips, dips, salsa.
Napkins, plates. You can get from the dollar store a box of those pool noodles as gifts for the party attenders ( in lieu of goodie bags), when they come in write their name on a noodle with permanent marker so at the end of the party they can find theirs. And let them have a fun time.
Make sure they all know that they can't leave unless it's with their parent.
Oh! and instead of cake do a decorated cookie it's easier to deal with than a cake out there.
Pool games. There are things that they can dive for. Tie a small ribbon around a dive stick and then throw them all in. Have the boys dive in and get the sticks and deliver them to the girls. The first one to get his to a girl wins a prize and the one that finds the stick with the ribbon gets a prize. Do the same with the girls.
Have them swim a lap and the first one to the other side gets a prize. Then have the best boy swim against the best girl and the winner gets a bigger prize.
For prizes you can go to Ross and get bath soap or lotions, scrubbies, things like that for the girls. You can get cool stickers for the boys at Tilly's or you could do pool type related prizes. Like sunglasses, sunscreen, lip balm, dive goggles, beach towel, inflatables. Things like that. You can make it as elaborate as you want and really not have to spend a whole lot.
If you need anymore help let me know, I have lots of experience being a party planner for kids. You can email me privately.
Have fun, this is a fun age and difficult all at the same time.