It's not too hard to write anonymously. There are linux distros like tails https://tails.boum.org/ which can get you on the internet, then just go to whatever blogging site you want and write. Hardware-wise there is the gluglug-x60 http://www.fsf.org/news/gluglug-x60-laptop-now-certified-to-... but almost any thinkpad from the last 5 years will run linux well enough.