I would strongly recommend that you physically remove everything possible before turning on the pump or adding chemicals. Fish everything possible out with a net. If you start pouring in chlorine now you'll waste a huge percentage of it just bleaching out leaves and sticks. Go slow and steady so as not to stir up the algae so you can see your progress.

When you do start to filter, take the advice above and watch your pressure like a hawk. The life of the cartridge will depend on how you manage the pressure. If the pressure builds up high the debris will get impacted deaper into the media of the filter and get harder and harder to wash out. When it gets really plugged, it's new filter expense time. For normal use a skimmer sock will help keep debris from getting to the filter in the first place, but that's no help when vacuuming.

You might also take a look at the "leaf eater" attachment from Rainbow. You can get it from the host of this site at
http://www.poolsolutions.com/cart/clean.php It's only $30. and will pick up lots of junk without even running you pump. You might find it elsewhere but Rainbow products are sometimes hard to find.

Good luck.