You can rent SharePoint 2013 direct from Microsoft, hosted in their data centres, for as little as ~£3 per user per month from SharePoint Online. Watch the quoted price though, as they like to play the old “excluding VAT” game.
I rented one of these for a month, just to try it out, and was pretty impressed. It sets itself up with a public site collection, intended to be your company website, and a private site collection, intended to be your intranet. The account admin page lets you distribute your user licenses via email.
For ~£10 per user per month you can get Office included as well, although SharePoint includes the Office Web Apps so you can do basic editing in the browser anyway.
Cancellation turned out to be a little more tricky. There’s no online cancellation – you have to deal with their 1980’s style phone system. For the UK the number was 0800 032 6417, 9:00 – 17:00 Monday -Friday. It only took a few minutes to get served, but when I did I learned that the subscription was for a year and that there is usually a cancellation fee of 25% of the remaining term, which would have worked out at around £25 in my case. I don’t recall that being highlighted during the “hurry! - buy now” process. They weren’t enforcing this though, so I didn’t get stung.
Impressed overall though and would definitely recommend the service to small businesses looking for online collaboration tools.