1. Get yourself a copy of SwissSys or any open-source Tournament director software. Really simplifies your life (takes care of tie-breaks etc.) and lets you worry about other things.
2. Going clockless is a little risky. You'll always have a few players who either REALLY use their time per move or worse yet, are just goofing away because they are losing and don't want to resign. Keep a few on hand and if the time alloted per game gets out of hand, slap down a clock with 5 mins on both sides and make it a sudden-death contest.
3. When you go round-robin, it makes sense to have them play both colors against each opponent for it to be a fair contest. Given that this is a scholastic event, why not drop the time/game and increase the number of games by 2x? Though this can get crazy for a single-day event! (too much chess!!!)
4. If this gets out of hand, I'd recommend the more common practice of playing top-seed vs top-seed and doing a double-roundrobin on that. That ways, you have each player playing 8 games such that.
Team 1, player 1 plays the Player 1s from the other 4 teams ... TWICE (once with black, then white) making it 8 games per player. Should not be overloading them for a single-day event if the games are quick.
5. Now if you can't seed them because they don't have ratings, might I recommend a quick tactical quiz over paper (10 puzzles, 10 minutes to solve them) and using the results to seed them 1,2,3 and 4? That might work.
Hope this helps!
If anyone has any advice on organising a school's Chess Tournament I would love to hear from you. I am a Teacher and have 5 schools from which to draw potential competition from. My thinking is 4 players per team, each player playing all other players once in a round robin team format (15 matches per player). I don't have access to chess clocks so recommendations regarding rules, format and scoring system would be greatly appreciated. First time trying something like this and want to get it right. Thanks in anticipation. Boris.