When you get to the US you may find that you get wads and wads of one dollar bills and lots of coin money.
I found that the 5c piece and the Quarter are very similar in size. So what I have done in the coin section of my purse is that I have one section for pennys (brown in colour) and five cent pieces (silver) and the other section is for dimes (small silver coins - 10 cents) and quarters. It's then easy way for you to hand over the right coins when it comes to paying for something.
When it comes to the one dollar bills - make sure you always have a few (say five dollars worth) on you, because you never know when you need to tip someone.