Screenflow is great if you don't want to edit in a different application (although you can if you want to.) However, if you plan on editing the entire video in a different video editor, you might want to save yourself some money and get something like Screen Mimic (that's what I use.) It only comes with the features you absolutely need so it is a lot cheaper.
BTW, if you don't already have a solution, it might be wise to get something like WireTap Anywhere so you can record the output of Logic without going through a mixer. Or you could always use a combination of SoundFlower and LineIn to get the job done. It's up to you.