You can buy a sump pump at many hardware stores. These are somewhat similar to the pumps used in ponds, and the smaller ones aren't that expensive and certainly useful to have on hand. If it's flooded once, it is liable to do it again.

a sump pump and a hose that leads outside, and a push broom or squeegee to push the water ahead of you...

I used Oxyclean powder to clean mine, actually, chlorine and I do NOT get along.

but getting it dry is more important, the longer it stays wet, the worse the problem will get.

First dump a quart or so of pool chlorine into the water and let it mix to avoid the mold porblem.

I would be wary about using electric appliances, like the shop vac, while standing in an inch of water. A sump pump draining into a laundry tub or the washer's drain line owuld work.

Try a garden pond pump. A sump pump has a 1.5 inch outlet and will not fit a garden hose very well. Even then, not many pumps can get down to one inch. A shop vac and a lot of trips may be the only good solution.