Shotgun mic: I second the Rode VideoMic recommendation above. That's what I've been using for years, mainly because I'm a cheapskate. I'd recommend the newest model because of the auto-on/auto-off feature. It saves batteries so much. My video test and review is below.
External mic: The zoom h1n1 is a fantastic option. Zoom is excellent and the price point is the same as what I use, the Tascam DR-05. The Tascam recorders are also a fantastic bang for your buck. The downside of course is having to align the audio and imagery in post when you're editing, which I'm sure you're well aware of course.
@Jskaanland : I'm going to embed my video reviews here. I am not affiliated with any of the brands I review.

Nor am I attempting to build my brand, gain subscribers, etc. This is for the edification of OP's question, and I happen to have just a wee bit of experience with field microphones while operating in rough situations.
And here is the Tascam (stereo field mic) that I film with. It's always in my camera bag, and has lasted all throughout Africa on multiple occasions.
Let me know if you have any questions. I love this stuff.
-Beau