Rick -- no matter what fat/oil you use, a food thermometer is essential. Your oil should be at 355-370 F. Any lower, and your batter will absorb it and become greasy; any higher, and the oil will begin to burn/break down/taste unpleasant.

Peanut oil is recommended because it can withstand high temperature. Olive oil will start smoking/burning before it's hot enough.

If you want to go the beef fat route, Mexican stores sell it in tubs (can't think of the name right now).

Beccy is right on about frying the potatoes twice, although I would up her temperatures by 15 to 20 degrees.

Cheers,
Michael