I will be attempting to bottle my first batch tomorrow. Is there any point in pouring from my primary into a bottling bucket through a sanitized strainer, or is it better just to siphon from the fermenter and not worry about the sediment?
Yep, what the others have said. At this point you want to transfer the beer are carefully as possible without introducing any oxygen. So, that usually means a nice siphon. Oxygen at this point can oxidize the beer and give you an unpleasant wet cardboard off-flavor.