Welcome to the boards!
RE: Sanitizing - If you are concerned, you can use a small dish with some rubbing alcohol to clean it off. Swish it once or twice, flick it off, and it will be ready to go. Most do not do this between shaves, but it can increase the life of your blades due to oxidation from left over water.
Re: Soap - Easiest and cheapest solution is to grab a mug out of your (likely) overstocked coffee mug cabinet and toss the soap in there. Put a dash of hot water at the bottom, throw the puck in, let it sit for a few minutes, and then carefully dump the water out. When the puck dries, it will most likely stay put when you are rubbing your brush on it. No need to transfer it to a soap dish, just leave it in the mug.
TJ, the DJ of Audible Odyssey, music of your dreams.