DO NOT buy the mini DVD... You will only get 30 min worth of recording.
If you are talking about a HandyCam type then go for the Hard Drive model or the memory card, just make sure you get either BIG enough to hold a bunch of footage.
The downside to the Hard Drives is that you need the computer to clear it, unless you delete it straight from the camera. The biggest UPSIDE to them is that every time you hit record on/off it creates a .avi type file and when you plug it into the computer you download them just like you would off of your digital still camera. They come off the camera ready to watch and can actually be imported straight into your editing software, if that's what you want to do.
If you go with the cards then make sure you get several of them and make sure they are big in memory.
Now if your talking about a Professional or Prosumer type camera then I would go cards or mini dv tapes.