I have a hood vented to the outside as well and I have only the aluminum mesh type filter. Nothing else. Every two months, I take the filters out and run them through the washer. I also periodically take the main panel off the hood (horizontal panel above the stove top) and do a thorough cleaning.
I have to buy new filters (2) every 5 years or so.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan