Don't know that there is a best of class for cloud computing yet, but Google has to be considered as a good place to start to learn and embrace the concept. Google Docs, Calendar, and Gmail are solid cloud type services.
Shared and private folders and docs are standard components. It's a free way to get cloud based, and then you can upgrade to business-grade service, like Premier Edition - $50 per user per year.
The biggest hurdle to overcome is weening yourself from Microsoft Office based docs. Google imports and exports, but it is not seamless enough yet, in my opinion. This is the big benefit of investigating MS.
As far as not having a server, I think you can move away from server apps to browser based apps, but you are always going to have a big box to store backups, etc. You can get away from server admin, but you aren't going to eliminate the desire and need to have a local fall-back.
Moving to the cloud definitely works for staff that is mobile or based in many locations. Great for home workers.