I started with a bit of hosted web space from 123Reg (Pipex), cost about £2.00 a month with a Domain Name. I used JAlbum (free Album Generator) to create the pages and uploaded them to the site. Good easy and customisable way to get purely a Photo Album website.
There are a few sites around that enable you to use their Gallery S/W, they generally have a specific look but some allow some customisation. I played with fotopic.net for a while, they have a free account and give you more options if you pay. There are many others.
I now use a site that enables PHP scripts and MySQL databases, I know nothing about either but they provide installers for various bits of software and I use Gallery 2.0 embedded in a Drupal Content Management System. The nearest thing I've needed to get to learning how to code is the ability to modify a CSS which I learnt through trial and error.
Have a look at
pendery.info | random thoughts
cheers
Dan