I rented my domain name in Gandi, using their mail service (details here.

Their infrastructure runs Debian, they support (with money and infrastructure) Debian and other free software communities, and they use Roundcube for webmail, which is actively maintained free software, nice, and has a mobile theme. I think there's also an Android app for Roundcube (I use K9, so not sure about this point).

I suppose that the 1GB limit can be overcome throwing money at it.