While leveling I put both mining and herbalism on my main character and send all the mats to two bank alts that just ping pong them through the mail until I'm done leveling. I save some of the mining stuff for leveling mining but most of it goes to a bank alt.

I get skinning and enchanting on a second alt.

Then at 70 I usually have enough stuff in the bank to power up any professions I choose in a day with enough left over to make a pretty penny at the AH.

Unless the quest with item pickups is part of a chain that is needed or has a really good reward I skip them.