As far as systems are concerned, Blogspot (now Blogger, owned by Google) is probably going to be the cheapest. There's no charge to use it, it's hosted by Google, and you can use a custom domain for free. WordPress is another free option, but there's certain features that you won't be able to use unless you spring for the $10/mo plan, and there's also TypePad, which starts at $9/mo and unlocks most features at $15/mo.
Some systems are going to require you host images elsewhere (such as Flickr, Photobucket, etc), whereas other blogging software might allow you to upload and host images as part of your package. Flickr doesn't limit display bandwidth, but with a free account it does have restrictions for how you can link to an image and has a monthly upload limit.
It's always worth it, in my mind, to document what you're doing and why. Who knows, you might be the first person to do the "zomg next mod that everyone has to do", and having it all documented on your blog means it'll be called "The Ben Mod"
