I’m unclear from the above whether LunarPages (I hadn’t heard of them before) are providing a virtual private server offering, where you get a Linux VM to manage and control the webserver directly. If so, Linode or Digital Ocean would be worth looking at.
Microsoft Azure and Amazon Web Services are the two dominant players in the cloud hosting market, and they both have Platform as a Service web hosting offerings if that’s more your bag.
If you’re looking for a simple blog style website, then WordPress is generally the go-to.
Edit: I’m posting from my phone, and it seems to have screwed up the whitespace around the links. Sorry.