For potato chips you actually need a LOT more oil than you think you do and a saute pan is nowhere near deep enough. A deep saucepan will work but you need it to be pretty wide so you have room to fry more than one slice at a time lol. Oil will need to be at least a few inches deep–you can reclaim most of it by not letting it get too hot while you’re frying up your stuff, then let it cool and drain it off through a fine sieve to collect any bits of potato, you can keep it in a jar in the fridge.
The only item that can be deep fried in shallow oil is a tortilla done flat to make tostadas, everything else needs enough oil to let the food float and cook without any crowding or it’ll come out funky and stuck together and not crisp at all.