Best Server Based Email- Hotmail, Gmail, ?????

I have a business that is expanding. Currently I use Outlook. Since there are a couple other people who also answer emails this program is great because it allows one to mark 'flags' with several different colors. This makes it easy for use to tell who needs to follow up on certain emails and which are done. It also has a 'checked off' option on the right...we use this when the email/subject needs no further attention.

Problem is that my assistant is now working 1/2 time remotely. So far, working with our website's basic server based email several emails have been accidentally overlooked. I am looking for a program online which has notations available like those on Outlook. That I know of, neither Hotmail or Gmail have these functions. There is read, unread, and responded to. We need more options than this as I mentioned above.

Any suggestions would be greatly appreciated. Thanks in advance!!