Can I use Office 2010 with SharePoint 2013?

Hi,

I have a client who is currently running SharePoint 2007. They have recently upgraded their office version to 2010 so they are now wanting to align their sharepoint version with this. Would I be best to migrate from SharePoint 2007 (WSS 3.0) to SharePoint 2010 (Foundation) or take it a step further to SharePoint 2013 (Foundation)? Is Office 2010 compatible with SharePoint 2013? Another option is SharePoint Online as their infastructure is dated. Will SharePoint Online (2010 or 2013....is 2010 still available?) integrate with their Office 2010 suite (Desktop)?

Thanks.