IMHO, the most economical method is going to be the turkey fryer with a high-pressure, adjustable burner. The low pressure burners are generally a large ring with a LOT of small holes in them. Sometimes they are not adjustable. These will not lend well to frying French fries or other high-water items.
A decent, high-pressure turkey fryer with a fry-basket shouldn't be more than $50. It keeps the stink/smell out of the house and has a GREAT deal more versatility. That would be my recommendation.
Regarding the best way to make French fries it's no secret that a double-cook with a chill in the middle makes them the best but I will go slightly contradictory to what was recommended up-thread. A few months ago there was a thread here that had a video on the quest for the best fish n chips ever made. In that video IIRC, the first cook was BOILING the potatoes similar to what you would do when making mashed potatoes, then chill, then fry. There is some sort of chemical change to the starches that happens when you cook them, then chill them before cooking again that makes a wonderful crunchy texture. It was determined that boiling vs. frying wasn't that big of a deal but the water lent itself to washing away the stray starch granules etc.
Of course, that is all from my recollection; it is my intent to try making those fries sometime but I haven't done so yet.