Currency Exchange Pre-trip

So I've been hearing several people say to order you Yen through your bank several weeks ahead of time, and don't wait until you get to the airport ATMs to get the best exchange rate. That's great advice.

What amount would is recommended to order for a 3 week trip? $1000 USD? $2000? More? I don't want to be foolishly carrying around a huge wad of cash, but I'd like to have enough to avoid the ATM for a while.