Here are the orb phases, you can also check the PDF below. It's a great resource that's continually updated:
Phase 1 (now): Black/Lightning/Dark
Phase 2 (start on 3/20): Power/Non-elemental/Wind
Phase 3 (start on 3/24): White/Holy/Earth
Phase 4 (start on 3/28): Summon/Fire/Ice
http://happypluto.com/~misterp/r/ffrk.pdf
Minwu refers to the FFII event that starts tomorrow, and runs until 3/29, which means it overlaps P1 and P4 by a day each. What I mentioned above was just what I will do to make sure I finish everything, while maximizing the orbs that I want.
As you may have noticed, if you're in the middle of a daily dungeon when the day changes, you get a notice that the daily dungeon has ended, and you're booted out. But the different phases of the orb fest dungeons are apparently treated as a single dungeon. Which means if you're in the phase 2 dungeon, and 3/24 6pm rolls around, it won't boot you out, and you'll still be in phase 2. This allows you to keep farming in any given phase even after its intended duration. However, if you exit the dungeon and try to go back in, it'll place you in the current phase's, because that'll be the active dungeon then.
P2 has Power and Wind orbs, which are by far the most important ones. So you want to maximize farming in P2, at the expense of the other phases. Even though you may be missing P1 and P3 orbs at this point, if you keep playing, you will, at some point, be short on Power and Wind orbs. You really want to load up on them while you can.
EDIT: Actually, for a new player like yourself, you probably can't stay indefinitely in the dungeon. Veteran players have Record Materia that refresh ability charges between fights, which means that they can stay indefinitely. So it's probably not an option for you, but it's not that big of a deal. However, it is absolutely true that P3 orbs are the weakest, so I would try to finish Minwu's event using P3 stamina instead of the others'.