What's the best way to get nice clean sound of the ceremony and speeches at a wedding?

Boom mikes, directional ones to be specific, and several of them. You could also hide hi-def wireless mikes in bouquets or something similar, It wouldn’t be hard to put a set of flowers on the altar.

If the space is not too reverberant, a couple of Crown PZMs closely placed (they’re flat, plate-mics) or other boundary mics, would grab the sound in a fairly open-sounding way; the shotguns are also recommended, but they can be very directional so aiming them becomes an issue and setting up multiple ones would be necessary unless you had a boom operator (which I take it would be impractical, after all, it’s not a movie set!)...I’m assuming if you’re miking multi-channel, a multi-channel mixer/recorder is in order…something like their R-series recorders: http://www.samsontech.com/zoom/products/multi-track-recorders/

Your best bet is, as you suggest, to take sound directly from the mixer for the speeches. For the vows/ceremony itself I would go with a high quality shotgun mic. the down side is that these are highly directional so if any of the parties that have a speaking part in the ceremony move out of the sweet spot you are pretty much hosed. You might consider hiring a helper to make sure the shotgun mic remains on target throughout the ceremony.