If you want to filter from the kettle to the primary, Home depot or Lowes, has 5 gallon paint strainer bags. Soak in Starsan and put over the opening of your primary Bucket with a bungie cord(s). (if you use a carboy, I dunno) that will help filter out the stuff.
It won't hurt to leave stuff in there. You will have to leave some stuff behind. It helps to let your primary fermentation go at least 3 weeks. It will compact better.
When going to bottle bucket, I start with autosiphon about 1/2 way down,and just follow the water level. I usually suck up a handful of yeast (not a lot) to ensure there will be enough for carbonation. (not sure if it's necessary, but don't fret if you get some in your bottle bucket.)