Though probably irrelevant now, seeing how this thread is 6 months old, I'll still respond for archival purposes.
I would recommend just getting a green sound guy that has some of this equipement. If he/she is willing to work for mostly experience, then you solve your budget issue. You're gambling on the quality, but I think it's a safe bet assuming you yourself, or a friend, would be operating everything that you buy/rent otherwise. To answer your question directly, there are only a few musts for sync sound (double system aka when you don't record straight to camera)...
1) recorder: look for at least 16bit and 48KHz in the specs and the ability to record .WAV files, as well as XLR inputs, and phantom power. NO .MP3 reocrders!
2) microphone: tons of reviews out there, but you'll probably want an all-purpose short-shotgun for the most balanced approach. Not going to be the best selection for every situation, but it'll do the job. The 416 you mentioned is pretty popular, but there are several other [higher end] options. My favorite dialog mic is a Schoeps CMC-MK41.
3) cables: to get the mic to the recorder, probably just one XLR
RECOMMENDED:
4) operator: someone who has used the setup you use on set before you actually start shooting with success
5) mixer: a decent field mixer will have much better preamps and limiters than a basic recorder, and you'll have much more control of the levels...tons of options out there, but what does your shoot require (number of people talking in one scene, for example)?