My grandfather had a stack of $2 he used to keep in a separate thin wallet. He called it his emergency money. His thought process was that $2 was the right amount of money to be able to buy just about anything without loosing much to change (say needing to buy a $20 item with a $50 bill and the person can't make change). He also liked $2 bills because some people treated them as being worth more than $2 due to their somewhat rarity. He could often buy something worth more than $2, just because the seller wanted a $2 bill. He also used to give them out as tips when he wanted people to remember him ("Hey, that was the guy that gave me a big tip in $2 bills, I want to get his table again.")

I do the same thing today, but on a smaller scale. I carry a few $2 bills and $1 coins in my belt (money belt). Really though $2 doesn't get you as much as it used to, so I'm thinking a stash of $5's or $10's a long with the $2's might be a bit more helpful. Also, I think he used to carry around $50 total. Today $500 would be needed to have the same buying power.

All in all, I think an assortment of bills and coins would be the most useful.