hmm, I don't think there are the best one, but the suitable one, which are suitable for your need, then you'll like it.
Usually I like use handbrake and Videora, both are totally free and do good jobs, you just wanna convert avi to mp4, I think the two can meet your need.
Well, if get special use or more effect like watermark or merge, then should turn to some other tools, maybe shareware. Recently I ran into a video tool named iFunia that do the update for iPhone 4, it's an all-in-one video conversion, can do nearly any conversion between videos, I think the upgrading is a good option for needing:
iFunia Video Converter adds iPhone 4 options | MacTech