I was only able to try these a couple of times in beta, as I haven’t been there long.
What you are asking about which heroes and/or teams to prepare is something none of us knows, as it can change every time…could limit you to only 3* heroes, and no reds for example.
One of the special rules sets all your heroes to very fast, so the slow ones may suddenly be your best heroes for that tourney.
You get five flags per day, but once you lose 4 times in total, you are done…with the option of paying to continue. What I felt was that if you lost 4 times in the first day or two, the continue wasn’t worth it. But if you are doing fairly well until the last day, it could be a good risk depending on where you are on the leaderboards.
I wouldn’t let it stress you out too much…it will be fun, and free to enter, so really not risking anything at all, as the tourney flags are separate from your regular raid flags…plus someone pointed out that the heroes you defeat in the tourney also help fill your raid chest.
So other than continuing to work on a good variety of heroes, including 3 and 4*, there’s not much else to do to prepare.