Essentially, there are two parts to your interaction with the e-mail system: your mail client and your mail server. The mail client (in your case Google's proprietary webmail interface) is the program you use to receive, read, and send e-mails. The mail server (in your case Google's mail server(s)) provided by whatever mail service you use is where e-mails from thousands of different clients are stored, processed, and sent on to other servers to be retrieved by clients.
There are two types of clients: offline clients and webmail clients. Offline clients (such as MS Outlook, Claws Mail, Evolution, etc.) are standalone programs which download messages from the mail server of your choice for you to read, and can also send messages to said server to be passed on. An online webmail client (such as the Gmail interface, RoundCube, or SquirrelMail) are mail clients hosted by the providers of mail services and accessible through a web browser. Most of the big corporate mail providers have their own proprietary webmail clients for their own services, like the Gmail interface I assume you use. RoundCube, SquirrelMail, Horde, and others are libre webmail interfaces. Many of the smaller mail providers use them (such as Openmailbox, Ruggedinbox, Riseup.net, etc.). Anyway, recommendations. I would have to recommend Riseup, which I am a proud user of. They offer POP, IMAP, and SMTP over TLS and SSL. You can retrieve and send e-mails either through RoundCube or an offline client of your choice. They offer 90 megabytes of online storage space for e-mails by default (though I reduced mine to make space for others because I use an offline client anyway) and the service is free of charge (though I would seriously encourage you to donate- they survive solely on donations). You can't just register for an account though- you have to apply. This is basically a political test, because the service is really supposed to be for facilitating activist communication and mailing lists. Though they warn of potentially waiting weeks for a reply, they underestimate themselves- I got my response the day after I sent in my application. On the client front- I recommend Claws Mail. It's fast, light, packs powerhouse functionality, has a nice interface, and is available in the Trisquel repository.
