I'll have to disagree with GreyFox7. There might or might not be an ongoing struggle between Google and Microsoft over compatibility between Outlook and Gmail/Calendar/Contacts/etc. This became critical for some users when Google discontinued Exchange ActiveSync for its free, consumer Gmail service. That left Outlook users dependent on IMAP for mail and eliminated access to the Google Calendar on those accounts. Google's implementation of IMAP is, to be charitable, non-standard. Outlook's implementation of IMAP is similarly non-standard. Anyone whose experience with Gmail is based on trying to use Outlook with it would be justifiably frustrated.
For paid Google Apps for Business accounts, which brocharlieb might be using, ActiveSync is still available but worked poorly with Outlook on the Windows RT platform. I didn't even try on the S3 because of a better alternative.
Because the S3 runs a full, non-crippled version of Windows 8.1, I was able to install the Google Apps Connector for Outlook. It runs between the Google server and Outlook, appearing to Outlook to be a pure MAPI server. For the past six years I have used that program on various Windows machines for several years and have never had an issue with it except the amount of time it took to sync my data the first time. Whatever battle there may be between Microsoft and Google, they have played well enough together in our company that I have felt left out when I read about everyone's issues.
I gather that brocharlieb is clergy. If his work email is provided by a Google Apps for Nonprofits account through his church, I don't know if the same kind of access is provided. I think it works, but I haven't tried it myself.
Accessing Gmail using a web browser, whether using Internet Explorer or Chrome, is pretty much the same experience on the S3 as on any other windows machine. Memory requirements have to be watched on the 2 GB versions. Using multiple tabs with Internet Explorer on my former S2 slowed it down, but the S3 just runs in 4 GB with six or seven tabs open. Because of its well-known memory leak, Chrome has to be periodically shut down and restarted. The S3 works better than the S2 for web mail because it is faster and can be had with more memory.