To expand on what Scott said, SharePoint Workspace (Windows or Windows Phone 7) only works with SharePoint 2010 versions.
You can certainly run a small SharePoint 2010 Foundation on less then 4 cores, but 64bit is a requirement.
Office 365 due out this year is a paid hosted service running SharePoint 2010 that -should in theory- support SharePoint Workspace the same as on-premise.
SkyDrive, the Microsoft consumer service similar to Google Docs, is said to start supporting Windows Phone 7 as storage for Office files once the phone OS gets an update later this year.