I think going back and forth between hand picking and taking first come first serve is a good idea. First come first serve helps ensure people who like your work can get a piece of your work - even if their character design isn't quite the most interesting thing to you - and hand picking helps make it fair across time zones and you get to ensure you have time to do commissions that really stand out to you as being exciting. The chances of getting jaded and falling behind are lessened.

I also agree with the person who suggested auctions. You could offer larger pieces that would bring in higher purchase prices that wouldn't normally be on a commission menu.