[Wlug] Web hosting

I know this question has gone around a few times, but I don't keep all the emails i get! Anyway, i host a weak little personal web site out of my house and was looking into hosting companies. Not quite sure how it works, if I want linux/mysql/wordpress. I need more than just a place to hold my index.html. Are there companies that give me total control over a "server" on the internet? I say "server" 'cause my guess would be a virtual machine I could control remotely. Any advise would be greatly appreciated. Mike