When kids are learning to count money, they need to be able to touch and count actual coins. These could include real money, or be realistic-looking play money, but children need the practical and tactile experience of working with the coins.
Whether you decide to use real money or plastic coins, make sure you have at least the following number of each type of coin:
You'll also want about five dollar bills to start with. As kids move into higher grades, you will want to add more paper money to your collection.
Play money is a great help with math homework, since coins are hard for kids to identify by a printed image on a worksheet. If these have been photocopied, it's even worse. Using coins to figure out homework can save your first grader a lot of frustration.
There's a lot of value in just letting kids play around with coins on their own. They might pretend to sell or buy their toys, or just count how much money they have altogether.
Some kids like to stack coins, or make pictures with them. Encourage kids to tell you how much their money-pictures are worth, or how big a 40-cent money train would be.
Most kids love money games. Look for board games, dice games, and card games that use money and are appropriate for kids.
Miss Brain's Cool Math Games (below) has fun money games for kids, as well as dice and card games for practicing other important first grade skills.
Finally, of course, don't forget the value of letting kids do some actual shopping, spending, and saving. They'll see the real value of money, and get real-life practice with their newfound money-counting skills.
You might also be interested in the article Counting Money Games.