Generally for both Andaz and Centric, I prefer taking the Tokyo Monorail Rapid Airport service which has luggage racks and takes 18 minutes to its terminus at Hamamatsucho (~500 yen/person). I then take the elevator down, where there's usually a taxi waiting at the curb, and from there both Andaz/Centric are around 2km away. Fares are typically somewhere in the neighborhood of 1500 yen but usually closer to 1000 yen.

The other direct and cheapest option with no luggage racks would be the Keikyu Airport Line straight to Higashi Ginza (~30+ minutes), finding an elevator, then walking to the hotel. It does get a bit crowded past Shinagawa depending on the time of day though one luggage shouldn't be an issue.

I've never considered the limousine bus since they don't service the hotel directly due the one lane streets beside the hotel, and between the walking and finding the correct bus stop, it's not exactly that much cheaper either.