When you pick up a crystal in the dungeon, do you:
A) Go for the biggest one?
or
B) Go for the biggest of your favorite color?
And if you have a friend who also shares the same preference as you, do you:
A) Try to beat them to the crystal for the lulz
or
B) Let them have it?
I always go for my favorite color, purple. I play with my boyfriend on skype and we pick on one another over who gets the big, purple gem. It's kinda comical and funny, especially when we get the same gem pool in the end.
Practically speaking, there is no reason to beat your friend to the mineral, because you both end up with each other's minerals at the end of the expedition.
If your goal is to earn crowns, then you should go for the biggest mineral you can find. When choosing between two minerals of the same size, you should favor yellow, green, and red over blue and purple, because the former often sell for 4 crowns per while the latter rarely sell above 3 crowns per. (This is based on multiple months of obsessively observing mineral prices.)
Alternatively, if your goal is to influence stratum themes, then research the theme you want and pick up minerals accordingly. I recommend saving up for a long time, or joining a guild that's into gate construction.
If you don't care about such practical goals...then choose the mineral that goes well with your armor/costume, and always beat your friend to it? :)
A) go for the biggest one regardless of color
B) Back when I was in party mode I would just stand there and let everyone race for the prize then pick from the leftovers. I got sick of everyone trying to snatch a crystal I'd just chopped down practically hunching my butt as I was chopping. I figure people get off on beating you and taking it from you so I just chose not to participate. I figure you can't get too much excitement "stealing" the prize crystal from the guy who didn't even try and obviously doesn't care. That was one of the many, many reasons I ceased running in parties.
I usually go for largest size first, favourite colour second. I always auto-sell so gate construction considerations don't really bother me.
I'm like @Volebamus, I avoid the colors I have a lot of and pick the others.
Size First (always)
Then Color
Color in preference: Green, Yellow, Red, Blue, Purple
Purple, I hardly use it. Trying to make beast and slime gates for my own pleasure.
Biggest usually, except for the one I have most of (blue).
Though there are many times my I pick up smaller minerals least collected color (Green). It's an odd complex of mine to make the quantities of all match, and failing bad since while 4 are in the upper 2800s/low 2900s, green's the odd one out at 2700s.