If you are a little techy then you could always try some DIY by buying a hosting package that supports MySQL databases plus a domain name of your choice. I use a service provided here by a company called Hosting Ireland (http://www.hostingireland.ie/
)who I find the most helpful of all those I have had dealings with in the past. This might sound a little daunting but to be honest it's got a lot easier over the last couple of years, indeed I can get a site up and running within half an hour nowdays, it's adding the content that takes the time.
Briefly the method when using Hosting Ireland is -
Choose domain name
Purchase hosting package to go with it
Select CMS application you would like to install on it, Wordpress is one example but I have also used Zen Photo and Coppermine which may be more suitable.
Ask the system to install it
All you have to do now is choose a theme and start uploading the images. OK, that's a very simple explanation and the getting to know the CMS can take some time but to be honest however you go about it you will need to learn how best to use whatever programme you choose. If you are not much into computers it can be a bit scary at first (although you can't actually break anything) but you will have a website of your own without advertising and customisable to your needs.