I have sensitive skin on my neck, like a lot of you, which is why I only shave every 3-4 days to avoid horrible breakouts/irritation. I happen to have very oily skin, too, so that's a double-edge sword. If I do shave everyday it leaves the pores open and causes breakouts. I have tried shaving every day using a brand new blade (VERY expensive) and that didnt help.
I'm currently running a Gillette Fusion with Noxzema shave cream. I get ~10 minutes of runtime per charge and the razor will last for ~10 cycles.