I'm with Gregor to some extent about the value of a photo blog, but I guess that's just me and where my head is at the moment. I've had a photoblog for 5 years now and it's the one site in my online empire which I increasingly find I lack the time or motivation to update. However, that's a personal thing and if I didn't have 5 years of archives stuck in it I may have moved to somewhere new some time ago and with that move may have come renewed enthusiasm.
For me, at my stage in life (busy job, busy family, max 2 hours per week to dedicate to online photo activities) I honestly don't think you can find a simpler, faster, easier host for your photo (or any other) blog than Tumblr (
http://www.tumblr.com). I've been using Tumblr for a couple of years now as a personal blog (
http://edwenn.tumblr.com) and I post photos to it every so often. I also pull them in from Fickle and from the
Filmwasters blog (which also runs on Tumblr, but which is really just a feed aggregator and not strictly speaking a photoblog). There are some pretty decent design template out there to turn your Tumblr page into a photo blog, but last I looked Tumblr weren't allowing comments. For some this is a major drawback. Other people I know for a fact actually enjoy the fact that comments aren't available. It's usually the deciding factor when people choose for or against Tumblr. In every other way it's ideal though, so take a look at that.
Regarding
Wordpress; I'm a huge fan of Wordpress and use it for my music website (
http://edwenn.com) and also my new, still being built photo gallery site (
http://edwenn.com/photos). You can sign up with their hosted solution at
http://wordpress.com/ or if you already have a web host you could install the Wordpress blogging software in your site and take it from there. All you need to do is choose a theme and get rolling:
http://www.teknobites.com/2007/08/30/photoblog-themes-for-wordpress/ Some Wordpress photoblog theme examples
http://www.kimwoodbridge.com/7-wordpress-photoblog-themes/ More Wordpress photoblog themes
http://tinyurl.com/npyora Google search result for Wordpress photoblog themes
Wordpress is probably the most complete solution from the perspective that you can customize every aspect of the way it looks and indeed how you as admin want to use it, BUT it can take over your life if you're an obsessive and unless you find a theme that you like 100% of you may need to know some basic CSS/HTML to tweak the bits you want to change (to be fair this last point applies to Tumblr themes as well).
Finally as some people here have suggested you could use Blogger or Blogspot or whatever it's called. Easy to use and set up, but to my mind they all look the same & while some of the photoblogs I visit the most use Blogger, I'd never set one up on that service myself.