Get in there, son.
Clear all the tops, and work from the top down. Keep the chain out of the dirt, and once you get to spots you are not sure about, get yourself a couple of the plastic wedges to keep the bar from binding. If you don't know what I mean, just ask.
Don't discriminate against the poplar. Think of it as tasty bread with your meal. Just mix a couple of pieces in with your denser wood loads, and it'll actually improve your burn. It dries in a year, and stretches out your burning time and versatility. And makes you a better person.
Most important, keep your body parts away from the chain, and the heavy pieces of wood as they roll and fall.
You can do it, just take your time, be deliberate, and stay safe.