I'm in South Florida and went through Hurricane Wilma, which dumped loads of tree branches and other stuff in my pool. A deep net leak rake was my best accessory. I had to lend it to a half dozen other neighbors.
On a day to day basis, I have a StaRite Great White suction cleaner, on a 19,000 gallon unscreened pool with many close by trees.
The best accessory you can get for your suction side cleaner is an inline leaf trap. I'm sure Josh, saltpoolguys.com, can tell you which is the best selling one as he can get them for you.
I have a Rainbow #179 leaf trap. Wish I had the easier opening #186 though.
I can tell you that this leaf trap catches a load of debris without plugging up your skimmer basket, pump basket, and filter. The clear body allows you to visually inspect when it needs to be cleaned.