Dedicated Hoster Incl. Good Mailserver & Global Connection

I am currently with a smaller US-provider where I am running a dedicated gentoo server with a dozen domains (all small stuff, mostly sme/private websites) and 2 dozen email accounts.

The nice thing about the current provider is that he lets me run sub-accounts where the holders of those accounts have their own billing. I let them run a domain/website on my server since its no extra cost for them, but they pay for the domain and extra email space for example w/o me having to care for it. They basically offer a minimum package and add every single thing on top of it, which I like since I do not need any webpage builders, templates whatever else. I rather only pay what I take.

Basically I am happy except for the connection speed, specially for the email. I am in Asia and other people using this server from Europe, and the time it takes to connect, up/download data to the server and to download larger emails is simply out of the normal.

any recommendations there? I am currently paying 75 USD/Mo + domain names. I think this is also a bit on the high side given that the server hardware is a bit out of date by now.

I am looking at the minimum to relocate only the email hosting to some faster service, which would have to have a reasonable storage size (>= gmail) with POP/IMAP access and of course to use my own domain names.