Joe, simple rule is that the closer you can get a mic to the source, the better. The H4n has good built-in mics but they may well be a distance away and you’ll probably get some wind noise (although the rather awesome RedHead windscreens will help minimise that).
You can connect an external mic to the H4n – best would be something like a Sennheiser G3 which has a lav mic on the subject and wirelessly transmits to the receiver that you’d connect to the H4n.
But if you want to retain the more mobile, dynamic option of keeping the mic on your rig then some kind of shotgun mic would be a step up from the built-in mics of the H4n – I use a Sennheiser MKE400 on my Canon 60D and am happy with it but others recommend the Rode VideoMic. For what you’ve described I’d check out one of the the Rode NTG shotgun mics with the SM3 shock mount as that’d be more directional than the MKE400 or VideoMic.