I don't use Twitter because I don't want to support centralized social networks, but I publish to my website much the same as others use Twitter - short links, notes, occasional blog posts:
http://minglis.id.au/
I post about technology, Australian politics, programming, privacy, and other generally interesting stuff. There are separate Atom feeds for each of the separate sections: links, notes or blog.
I'll get around to setting up POSSE [0] to Twitter some day - I'll have to move off Github Pages first.
[0]: http://indiewebcamp.com/POSSE