If you are talking the 2011 MacBook Air, either version will run Handbrake and Parallels just fine. I'd recommend getting the 4GB version (which all but the base 11" have). The Sandy Bridge processors are very good at handling these programs, which are CPU-intensive. Be aware that running Handbrake will cause the fans to speed up very quickly, though. During a DVD encode, the CPU will likely hit 90 degrees Celsius or higher (max is 100 so it's still OK).
Note the 2011s don't ship with iDVD so you'll need to migrate it from an older Mac if you want to run it.