Can't help with specifics but check combos via Ninja > show combos; maybe write it out and test it against Kakashi's clone in Konoha. As for summons, if your team has a gap combo-wise (say, your combos always end at Hinata's chase (causes knockdown), use a summon that takes advantage of knockdown. And mysteries depend on the team too, but the one that causes sleep is pretty valuable.

My personal strategy is to stall with clones/shields until the rounds go by and I can set opponents on fire again :). I have Great Ninja War Kiba, Kakashi, Kabuto; Kakashi is really squishy though so I use him to stall until my main can get through both uses of Dragon Flame before you have to wait 4 rounds. Meanwhile Kabuto keeps Kiba/main alive and Kiba autoheals Akamaru and himself. You could go for a pure damage or pure defensive team. Whatever feels right~

Hope this helps!