Well, the "proper etiquette" dictates that only people named on the "inner envelope" of an invitation are actually invited. (So if "and Guest" or a boyfriend/girlfriend name doesn't appear, the invited person should not assume that he/she can bring a date; likewise, only children specifically named are invited.)
However, you will almost certainly have people who ignore this convention or think you're being "rude" by not allowing dates for single guests. In my case, I had a (*****y) first cousin tell her mom that she "lost" her envelope and wasn't sure whether she was allowed to bring her boyfriend. (A boyfriend I had never heard of and had never been to any other family events.) Anyway, her mom called my mom, and my mom said she could bring her BF.
Now, one thing you could do to encourage single guests to come alone is start early with efforts to coordinate roommates. We managed to pair up most of our single friends as roommates, which worked really well, even when they didn't know each other beforehand. It let them split costs and gave them somebody to eat meals with, travel to parks with, etc. I think that particularly since your friends are so young, you could really sell this idea as a way to help them save money. You'd still need to decide whether you want to give them the "and guest" option, but if you do give them the option of the date you could still encourage them to go solo to save money.
Another thing we did was use the save-the-dates as a sort of pre-invitation. We had a pre-RSVP deadline and a request for guests to email us by that date if they were coming. If at that point a single guest said he/she was coming but didn't indicate a boyfriend ("I" vs. "We"), then we didn't feel badly about not putting "and guest" on their formal invitations. We did get a few who said things like, "I plan to attend and will hopefully have a date with me." We gave those guests the "and guest" option, but as it ended up, the save-money-with-roommates offer worked so well that we didn't have any guests at all who brought non-serious-significant-others as dates.
Sorry for the long-winded response. I know this is a tricky issue. For us, it was the cost and worries about exceeding the maximum capacity for the Living Seas that made the "and guests" stressful. Good luck!!