Well, I'll assume your DAT machine has a mini-plug mic input (as opposed to an XLR mic input).
I've been using a Rode Videomic, which is a shotgun mic costing about $150. It works very well. If used outdoors in any sort of breeze, a shotgun mic should be used with a fur "wind muff". Rode sells an affordable one called a "DeadCat" for its mic. If your subject is some distance from the camcorder, then a mic extension cable and a mic boom (and maybe a boom operator) would be needed. BTW, a mic boom coud be just a $4 bamboo pole with a 1/4" bolt through it.
If your subject is going to be some distance from the camera, and moving around, then a wireless lav makes more sense. Azden has some reasonably priced mic/xmtr/rcvr kits.
Hope this helped, :)
Ken Hull