Improved Clinch is a good, simple, fast knot. However, I've been using a modified version of the Uni Knot lately for Mono, FC, and braid and have been loving it. Start by wrapping the line twice around eye of the hook then finish the Uni Knot as usual with 5 wraps for Mono and FC and 8-10 for braid.
As for the swivel... I'll use one if I'm fishing an inline spinner (which isn't often). I'll use just a Duo Lock snap for crankbaits (no swivel though). Other than that, I tie directly to my lures.
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