It depends on what you want to do exactly lucky.
A lot of people who are interested in photography have a photoblog which displays their pics generally a photo at a time.
Then you can also go for a more professional type site with lots of galleries etc.
If you arent interested in paying for space at this point in time there are plenty of free journal/blog sites out there which u can use as your basis for a photoblog.
I use Diary X and used Blogger before that. These types of sites are hosted by those companies and you could have a url such as :
If you have your own space you can download great programs like Moveable Type or B 2 and do the same sort of thing under your own domain.
As far as building your own site without blogging tools, there are many free hosts out there that offer you a certain amount of space with a catch. Most have pop up ads but you may find some with a banner up the top which isnt as annoying.
Thats why blogger was good because they had a banner up the top and diary x even better because they have no advertising!
I do really like diaryx but i have my own site now and Moveable Type powers it, so once i get around to it i will be transferring my photoblog to MT. My site is hosted by DreamHost which are very good and reasonably priced.
If you are looking for a good host, check out ServerFly. they have good prices and good service I hear. For a photoblog I think Moveable type is the best right now. I would watch the development of [url="http://www.wordpress.org]Wordpress[/url] though. The main coders have taken over the main b2 fork. I am hoping they make a nice photoblog script within their next release.