First of all do not worry about the hop residue, trub etc... It's not going to hurt your beer and it will settle out in the primary.
Second. A screen is useful. I use a bazooka screen on the inside of my kettle. Note: I also use leaf hops. For pellet hops, you might consider something like this
. (In the first post, the pictures have been deleted, but you can read through the thread to see them all.)
For siphoning, you should invest in an autosiphon. A regular siphon will work too. Just make sure the carboy is higher than the bottling bucket.
I think I hit all of your questions.