Considering getting a deep frier
Because of the rampant "discovery" of Peanut allergies, I would out peanut. Canola is fine, but can be expensive. Grape seed has the highest smoke point of the three. I would go with grape seed.
It depends on what you are cooking as each oil will inevitably carry some flavor but smoke point is really where you need to be concerned. For example olive oil is not a good frying oil, although you can use it if you are careful. For highest smoke point go with grape seed. But for Asian flavors peanut oil is not a bad thing---especially when combined with a little chile oil.
I'd go with peanut, myself, assuming you're doing home cooking and have no one with allergy issues in the household. Canola works alright and is the least expensive option, but it has a fishy smell when heated (from the linoleic acid in the oil) that can be detectable in the fried food and definitely lingers around the house, post-frying.
Grapeseed oil is indeed an excellent choice for high-temperature cooking because of its high smoke point, but at $10 for 16 ounces where I shop, I'm not going to fill a fryer with it.
Peanut for me.
Canola to my tastes when used for frying imparts a fishy taste and smell to the food.
(oh, I see Sfmiller has had the same problem with Canola 'fish smell').