The sum of the team's init.

The lower one goes first, which will be overwritten by the higher one. So higher init is better.

Just to emphasize because i first i had trouble understanding this as well.

It's the sum of the initiative from ALL your active ninjas that count. So the initiative of your move 1,2,3 AND 4 ninja added up together.

The team that has the higher initiative overall gets to keep their barrier.

The position of your ninja or initiative of the barrier ninja wont get you the barrier if you loose it to anothet team. You need to increase the initiative af your lineup.

What effects your stats in arena then?

Your regular init (or a portion thereof) is carried into arena. And since init only matters in relativity, regardless of if it's all or just a portion, it'd be the same. So... your actual init.

Not just initiative, all together. What effects stats in Arena? Does Mood? Does Eight Gates? Do stars? Does awakening or cultivating? Armor? I know Battle Armor does because people with special costumes always have higher stats, right?