Don't overcomplicate things.
For your first brew, this is how bottling day should go:
- Sanitize everything you're going to use (bottles, bucket, spoon, siphon, bottle caps, bottle filler, etc.) P.S. If your kit says to boil your bottle caps, this is not good practice. Instead, sanitize them in a no-rinse sanitizer and leave them in it until you cap the bottle.
- Boil your priming sugar (if using 4 oz of sugar, boil in 2 cups of water) for 10 minutes.
- Transfer to your bottling bucket after putting the priming sugar in it.
- Transfer from bottling bucket to bottle and cap.
Don't worry about crash cooling or adding anything other than the priming sugar--it's extraneous much of the time, and is absolutely unnecessary to concern yourself with in your first few batches.
As for how you keep the trub out of your bottles, it's easy: You'll have a racking cane that goes to the bottling bucket. This cane will most likely have a cap at the bottom designed so it doesn't suck up trub (the stuff at the bottom of the fermentor). Keep the top of that cap in liquid rather than trub, and not much will get in your bottling bucket. Then, you get a similar trub-avoidance from the spigot in your bottling bucket.
The furthest I'd recommend going to avoid getting particulate in your bottles is to move your fermentor to where you'll need it several hours before you do anything to it so everything that gets disturbed settles back down.
