More important is that the bills are all new, no tears/folds/crumples etc as if they have them, people prob will not accept them here.
As for counterfeit - I don't know that it's a huge issue with counterfeit dollars (pesos can be a problem occasionally). But if you have a US bill around, bring it with you for comparison sake.
I wouldn't recommend anything smaller than $50 USD bills and $100s are probably easier. Less to carry. And again, smaller than $50 bills, people may not want to change here if you're planning on using the dollars here.
What is the deal with the Latin People for its obsession on insisting for a brand new Dollar note when doing the "Cambio"..?
I was in Peru, Lima, last year and when I went to exchange a few hundread dollars into their currency,every Cambio place were insisting and almost seems obsessed for a perfect Dollar bill, No tears in Dollar bills or no Good, I had so many times being refused US bills that weren't perfect. In the USoA, I can use any denomination bills with corner of the bill missing as mutilated and so on but still OK.. In Latin America, if the USD$ bills aren't perfect, in some places saz, I will exchange that non-perfect bill but,..I will give you only 90 cents on the Dollar, etc,etc.. Why is that? Some people said,(merchants mostly ) if you take a non-perfect bill into the Bank for deposit, the Banker will not give them a full value for the US Bill rendered..?? Is this practice in BsAs the same? Do the Cambio places insist in new or newer perfect USD BIlls only.? In order to get a almost new Bill note at the Banks here in CA is almost impossible..The Bankers said, it is almost impossible to give you new Bills,unless, it is the day that the Feds will send a new Dollars infusion to its borrowing banks. I have been advised from established Ex-Pats in Peru, to bring new or newer looking USD, with no rips or too old denominations,He said 'cause you won't be able to exchange them here.! Indeed, the "Cambio" places did give me a hard time while trying to exchange, a few hundread Dollars in my pocession but not all my cash weren't looking new Bills..
If you were in a Non Dollar currency economy country and you had to take a trip abroad, you can go in to that Bank and ask them that you need foreign currency in USD denominations. For instance while back in Tokyo, I went to a local Bank and asked if they handle USD$ and they said, available. I have bought a Japanese Yen, 800.000, which at the time exchange rate it was about USD$1000.00 and all the Bills were "Spanking New"! You can get brand new USD$ Bill in foreign country but not here in America..