In the vast majority of cases, ServInt doesn’t recommend using WordPress caching plugins in conjunction with APC. Caching to disk, which avoids PHP interaction, is much more resource efficient in most circumstances. With WordPress and all CMS software, the most CPU usage happens when PHP is hit. By setting your caching plugin to “disk cache” in the plugin preferences, you cache your php pages to HTML and then serve the HTML to the end user.
If you still wish to use APC, be aware that with recent versions we have seen the out-of-memory errors become more and more prevalent no matter how big you set the cache. It all depends on how much data APC needs to cache. Limiting the number of domains or number of files that you cache is probably the best answer but will be very site specific.