The maximum rate of meteors expected to be visible is around 5 per hour (ZHR). However, this assumes a perfectly dark sky and that the radiant of the meteor shower is directly overhead. In practice, the number of meteors you are likely to see is lower than this, and can be calculated from the ZHR formula.

The Moon will be 9 days old at the time of peak activity, presenting significant interference in the early evening sky. (via In-The-Sky.org)