From experience Clamwin and avast had higher false positives than some of the other free options. Microsoft security essentials had lower false positives but its also not as good as avast at detecting actual viruses.

There are a few antivirus comparison sites you can can check out to see how they handle false positives. if you go to av-comparatives.orghttp://www.av-comparatives.org scroll down to reports and select charts and statistics http://chart.av-comparatives.org/chart1.php. From the test drop down take a look at the different types to see how different antivirus's compare. Once you select false alarm test you'll see which antivirus's are more prone to them in their tests.

av-test.org http://www.av-test.org/en/home/ also does its own tests but they bundle false positives with scan times,etc under usability. You would need to sort by usability, then click to each one see its specs.

The goal would be to find an antivirus that does well at everything. Detecting virus's but also is not prone to high amounts of false positives (many antiviruses will have false positives from time to time)