at random, randomly
Names were picked at random out of a hat.

out
He was picked out as the best player.

as
They picked Jane as the captain.

for
Have you been picked for the team?

freshly picked
freshly picked strawberries

carefully, gingerly
Rather gingerly, George picked up the tiny bundle.

absently, idly
I idly picked up a magazine and leafed through it.

gently, slowly
She gently picked up a plate and examined it.

hurriedly
I hurriedly picked up the receiver.

try to
bend to, bend down to, stoop to, stoop down to
She stooped down to pick up a stone.

by
He picked the pan up carefully by the handle.

from, off
She stooped to pick the book up off the floor.

Pick is used with these nouns as the subject:
judge, voter

Pick is used with these nouns as the object:
banana, berry, brain, card, coconut, cotton, fault, favourite, fight, fruit, grape, herb, jury, leaf, lettuce, lock, moment, mushroom, name, nose, number, outfit, pocket, quarrel, spot, successor, target, team, tomato, topic, vegetables, way, winner, word