So generally speaking, most smaller microphones won't be super-directional, but still might get you better results than the built-in stereo mics. If you're recording a distinct sound source from a few feet away, a condenser mic should be just fine. However, most decent shotgun mics will be fairly large; I'm not sure if a cheap small one would be worth it.
I use an Audio-Technica AT4041 for a lot of my on-the-go recording, though mostly for voice performance and foley directly connecting into my I/O device to a computer. Here it is for comparison (on top of its case) next to an H4n:
Generally speaking, I'd definitely recommend having something other than the Zoom's built-in mics for on-the-go recording. The stereo mics are originally meant more for live band recording, and they're good for picking up background recordings, but obviously aren't ideal for all other situations. If you can generally record pretty close-up, I'd look for a decent condenser mic that fits your budget.
On the editorial end, do you have any denoise options available? Rather than putting a ton into a mic that you'll be carrying around with you a lot (and thus might potentially damage or lose), it might be smarter to split the difference between an okay, modestly-priced mic, and then some software you can use to clean up unwanted noise out of your recordings (which is also just really useful for dialogue and effects editing in general).