...but Blogger is run by Google, your concerns wouldn't be an issue...
I don't know about wordpress...
However, Wordpress is both a hosting company and free software that you can run on your own hosting account...
If I had to guess, I'd say that Google was more stable than Wordpress (out of sheer scale) but hey, the DU goes down every now and then, eh?
Between these two, I don't know anything about advertising / banners / etc (like the old 'geocities' days). I don't see any ads on either one, so I just don't know how it works...
...considering they're free, I would sign up to both and see which interface you feel more comfortable with.
I should add that
http://www.typepad.com is very popular among professional computer people, but it's not free. I know that Amber McArthur
http://www.ambermac.typepad.com (
http://callforhelptv.com ) runs her blog off of typepad and that she would probably not do so if there was any doubts about it. It's $50 a year, however.