The software used on this site is WordPress, it is one of the most popular blogging and web-site development platforms. The software can be installed on a multitude of providers, both free and paid.
I am writing a series of articles on WordPress for this site, and will hopefully include some helpful information in them.
I use an instance of WordPress that has been installed on my 6Sync virtual server, called Erebus. 6Sync provide an excellent service and I can recommend them for competitively priced virtual servers on modern hardware, they are also based in New Zealand of all places which is an added bonus, even though their servers are in the US.
I host a number of other web sites on this server, including a couple of other WordPress sites, web and twitter analytics, and other bits and bobs. I find it very useful to have a server that is always available that can run various scheduled tasks at high speed, this means that servers that I have at home can be both low powered and intermittently connected without causing any issues.