Of all the tech changes I've made in the last few years, moving from Google Apps mail to Fastmail is the one that's made me the happiest, every day.
The webmail is absolutely amazing. So fast, rock-sold, clean, minimal, focused.
Having your webmail experience be completely ad-free and snoop-free, and, well, Google-free is priceless.
Choose the Business email option - https://www.fastmail.fm/signup/business.html - if you want them to keep an automatic archive of the emails you download via POP. When I signed up under the Personal Email option I found they didn't have this archive option, but they switched me over to the business account on request.
It's so worth the measly $15/year, considering the importance a good email/webmail experience, and how much it affects your every-day life.
I've helped a few friends switch over, and they've all been thrilled with it.