Cisco recommends between 12-24. By default, the WLC has a limit of 12. You can change this by doing the following:
Go to Wireless -> 802.11a/n -> General -> and under "Clients (1 to 75)", you can increase the number. Do the same to 802.11b/g/n.
Please note that the number of clients that are saturating one particular AP, the slower the throughput. And try to avoid designing/deploying only one AP in a high-density environment and consider disaster recovery.
Before you even consider purchasing the quantity and the model, please have thought about conducting a Wireless LAN Site Survey.
For the client limit setting it shows this is the setting for traps. Is this just setting the threashold to alert you that greater then X clients have associated? This does not appear to be a hard MAX setting. Am I wrong?