I agree with KlausKesselGO. Learning to code your own site is the best way to do it. It doesn't cost you anything to learn it. There are lots of tutorials out there like Kluas said, you can use w3schools or you can use html dog (google html dog) w3schools is a good place to learn but it's very boring. Html dog make it interesting and it's the basics.
I think coding it yourself, although difficult, is the best way to go. No branding, and a lot of freedom. Just go to W3schools.com
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what do you mean by fully functioning? wordpress is actually a good cms and it's easier to learn. but that depends on what 'fully functioning' means.