What is a good web based email client?

I dont think you know really what you want. Considering outlook and thunderbird are pulling mail from web based emails. I would suggest using gmail in an IMAP setting vs a POP3. As an IMAP you can still forward your email to a program like thunderbird or outlook, etc. but still keep it in your web based email so incase you are not at home you can check it elsewhere. So yes you are interested in gmail or yahoo, and I HIGHLY SUGGEST GMAIL for what you are wanting to do.