Plectrums (picks)

You probably think this is completely irrelevant and not important. Trust me, it makes a difference. Choosing the wrong pick for the wrong song could ruin your performance. If you're good enough it might not change that much, but you should always be trying to match your pick to the song you're playing.

For playing pretty classical things or chords you should definitely use soft, bendy plectrums. They will make you sound smoother and generally nicer, whereas a hard, thick pick would just not work as well. 
For shredding and fast playing in general, you should use thick picks or the very small thick picks if you find them more comfortable and easier to play with, which some people do. The thick picks don't bend so you have more control over what you're playing which you will need when you reach super speed. Soft, thin picks will not allow you to play as fast without making mistakes and sounding clean.

If you play bass guitar, you need to get a bass pick. They're wider than normal picks and are easier to play bass with.

The brand of the pick doesn't really matter as long as you feel comfortable playing it.