There are several things you pay for when dealing with a Webhosting company. The first is the amount of disk space they allocate to you. Do you need 100MB or 1GB? How many files will you have on your website and how large will they be. Again this isn't etched in stone as most Webhosting companies have several different plans with different amounts of disk space and different prices. The same situation applies to the amount of data you expect your site to have to transfer. Do you need 1GB/month or 15GB/month? Again you can usually switch, so maybe the best idea is to start small, and move up to a bigger allocation if you need to.
Another factor to consider is what services you may need. Do you need to be able to run a database application, and if so does the Webhosting company support the database you want to use (e.g. MySQL or Access). Similarly does the site support PHP applications, ASP applications, Perl scripts etc. You may not need any of those to start with, but if you do make sure the host offers what you need. Again you can always switch hosts if later on you find you need something your current host can't offer.
This website is hosted at HOSTMONSTER (see above). I looked at a number of companies and Hostmonster seemed to be offering the best deal. For $6.95/month (paid 2 years in advance) I get unlimited disk space, unlimited downloading bandwidth, 100 MySQL databases, 5000 email addresses (which I'm not really likely to need), plus lots of utilities such as web traffic analyzers, blog software, forum software, photo gallery software etc. which is all really simple to install via the Fantastico interface. Fantastico is a system which automatically installs other programs on your server. You don't need to get involved in the setup process, which for these programs can be pretty complex. So far Hostmonster has been pretty good. There have been a couple of small outages, but they kept me up to date with what was going one (in once case a local power transformer was struck by lightning!). Whenever I've called them I've got a live human on the phone within a minute or so, and that live human has been knowledgable and helpful. I've previously had some smaller sites hosted with companies who were impossible to reach or took hours to reply to a message, so finding someone who is responsive is a big plus.
Of course there are lots of other webhosting companies. Pricing for hosting runs from maybe a low end of $30/year for a tiny site with a small amount of data transfer, up to $1000/year for a large site with a dedicated (rather than shared) server - that means you get one their computers all to yourself. In practice the hosting fees for a small or even medium traffic photo website shouldn't amount to more than $100/year. Checkout these companies and see if they have a hosting package that sounds right for you.