Hi DITW,
I do this kind of thing as a sideline (setting up blogs/websites - not blogging). Wordpress is ace. You can get it for free, but your blog address will be deepinthewoods.wordpress.com or something similar.
You mention that you'll be using it for work. In which case you may not want wordpress in your address. If you already have a website it is easy enough to install wordpress under the same domain name, so you could for example have it at deepinthewoods.com/blog. It shouldn't cost too much to get it installed for you - it literally takes a few minutes. The time consuming bit is making it look pretty, but there are thousands of themes already made and ready to use which you could install yourself.
To give you an idea of cost if you're looking around, I charge £7 a month or £70 a year for hosting, and I'm at the end of the phone if there are any problems...