Premiere Pro is a great bet, but there aren't too many people who drop $1,800 to edit cell phone videos.
Truth is you may have trouble finding and editor that will be happy to take these files. M4V is an acquisition and delivery format. The long GOP (group-of-pictures) structure it uses is not friendly with editing programs. In order to draw a single frame the computer may have to draw 30 other frames, sometimes both ahead and behind the playhead. Long GOP codecs take a lot of computational horsepower to work with, so transcoding to an editing format such as DVCPRO HD may be beneficial.
That said I'd try Lightworks. It's an open source NLE that's Oscar and Emmy award winning. Windows only for now. It's codec, rate, and size agnostic, so you should be good to go. I haven't used it at all, but it looks pretty good. Someday when I invest in another PC or when it comes over to the Apple side I'll check it out.
Here's their list of Hollywood features that it was used in the making of; I'm sure you've watched a few of them.