You might have to check two bags if you're going with an airline size suitcase. When I pack up my Surly LHT with front and rear racks, panniers in fenders, I'm relegated to a full size bike box, and even then it gets a bit cramped. You will also want to make sure you pay attention to the weight of the suitcase. You'll get hit hard with extra fees if it's over 50 pounds. When possible, use clothing to pad the bike, and take as much as you can with carry-on luggage.
I'm sure you've checked already, but take a look at the allowed baggage dimensions for different airlines, as well as charges for bike boxes. Right now it seems as though smaller airlines, such as Allegiant Air, Mesa, and Alaska Airlines, are still around $50 each way for bike boxes. The major airlines (Continental, Delta, United, etc) can charge up to $150 each way.
If you decide to take the bike box option, here's a link that might help that process go smoothly: http://www.adventurecycling.org/features/boxingbike.cfm
As far as insurance goes, I'm afraid I don't have an answer for you, but you can take precautions by putting 'fragile' tape on the bags before checking.