I've no idea what the healthiest oil is, if you believe saturated fats are bad then beef dripping probably isn't for you, but it makes the best chips. I think as long as you're not eating huge amounts of them it should be fine. If you cut them thicker then you'll get lower fat chips. It can be mixed with rapeseed or sunflower oil. Lard (pork fat) works too, but I can't stand the smell, it has a lower smoke point than beef fat. You probably want to cook them at up to 210C/410F so best not to use a fat with a lower smoke point.
You should change the fat fairly often too, rancid fats are probably bad for for you, and they taste & smell horrible. Some fats go rancid faster than others.
Don't use olive oil for deep frying, especially not virgin olive oil, or coconut oil, it'll make a lot of smoke.
Rapeseed oil works pretty well, just it wont crisp the chips as much & it's tasteless. Sunflower oil has a bit more flavour. I don't like palm oil. I think duck or goose fat might only be marginally better than lard.
There's some information about different oils to use for frying, aimed at US food businesses here...
http://fapc.biz/files/factsheets/fapc126.pdf
You should avoid solid (hydrogenated) vegetable oils due to trans fats.