Legandaries

I'd highly recommend using a Ultra Ball for those three. Use a Dusk Ball for Uxie and Azelf since you fight them in a cave. If you still have the Master Ball, use it on Palkia if you want. You can also use the Dusk Ball on Palkia when it's night in the game. Hope this helps you out.

Quick ball, Timer ball, Ultra ball, and Master Ball.

All I know is that cyrus gives you a master ball use it on palkia

Well obviously a masterball if you have any but I would recomend a dusk ball for uxie and azelf and palkia I caught it with a dusk ball too while it was at night so I would wait till then and try and catch him if not try a tactic of stalking up alot of pokeballs and timer balls and keep using the pokeballs and then when you get them in red use the timer ball