I rake up after cutting and save the mess in tubs for kindling. Bark, chips, sticks, noodles, shavings, splinters and all.
I drop and handful in the fireplace and stack a few well place logs on top/around the little pile and hit it with a self starting torch, after pointing the lit torch up the chimney for 10-20 seconds to get a draw started. A good combination getting to the quickest, easiest, most effective method I've found.
My wife doesn't like the sound of the torch and prefers the old newspaper under the grate method her parents have used for half a century. Her's often start out a bit on the smokey side, but I dare not tell her she needs to heat the flue...