How can I save my gmail messages somewhere so they are safe? Outlook?

My messages older than a year or so get deleted from gmail. Also gmail keeps threatening that my mail is about full and will stop working. Yet I still need to access my email from any computer.

I need for my mail to go to a safe place. Is there such a thing as an outlook email server I can access from many Windows computers?

Or could I have Outlook or Thunderbird on my one office machine, and have my gmail messages constantly downloaded to this one machine?

I'm really desperate for a solution. Thanks for any help. I would also really love to have the features Eudora had, but still be able to access email from any of my several machines. I have a site license to Outlook and Thunderbird is free but I don't know if these are solutions. I would like to keep my gmail address but that can change if needed. I'd like to use Gmail as an IMAC server, like I used our company mail server as IMAC with Eudora. I'd have IMAC delete read email after 1 month, in which time it would populate to all my computers.

I also need to synch with my Android phone.

Jim

Golden, thanks so much!

Can I do this with gmail. so I can still keep my gmail account?

Thanks.....