If it's a .co.uk (or .org.uk) domain, then I'd recommend 123-reg.co.uk (if looking at others, should aim to pay under 10 quid for domain registration).
daily.co.uk is also used by some (have not yet tried them myself) and seem low cost. I tend to get hosting separately in case of any disputes over fees (or a sudden increase, as happened one year... by keeping the registration separate I could switch to another hosting firm by changing one of the settings in the domain registration control panel).
If you're after something like a .org, .com or similar, there are plenty of competitive prices. I'd check GoDaddy.com, MyDomain.com, Name.com and NameCheap.com Prices range from around $8 to $14 per year for .com, org, net, info (though sometimes there are deals hence worth checking a few competing services).
Rather than pay standard 'renewal' fee, look around after 6 months for any 'transfer' discounts, they add a year to expiry date when transfer completes, and it's usually 20-50% less than paying most renewal fees.
Lots of options for web hosting, and e-mail, and it should be quite easy to provide you with e-mail forwarded to some suitable account (eg GMail as NN has suggested) while having web site on wordpress.com if that's what you decide, or using web hosting...
(I host for clients) and there are freebie packages (to set one of these up usually requires a two or three page web form to let you enter your name and mail address, site description/name [a longer form of what your chosen domain name stands for] and a few other details).
There are free photo galleries, blogs, etc available for installation, and it costs nothing but some of your time to try different ones out until you are happy.
Have a play with wordpress.com and if you decide that will do what you want buy the domain via them. I recently transferred a .com domain from them to tsohost and it was relatively easy, so wordpress.com is as good a place as any to start at given what you want to do. You could setup a gmail account for the email perhaps.
How big? Depends on the image sizes. Start with the free account. Then get a feel for what size the images are (filesize) for displaying well on various devices, then multiply by how many you expect to upload. Also consider how popular your site will be, many webhosts will give you ample Traffic limit. They will often tell you if you are getting near the limit and offer upgrade options. The more Traffic your site gets, the more it will cost you. But do not worry about that at this stage.
I would start by creating a free account at wordpress.com, setting it up with a free theme that wordpress.com provides and have a play. Google for tutorials on how to use wordpress if you get stuck.
See if wordpress will do what you need, then decide if you need a paid theme or not and if you can comply with wordpress.com terms or if you need commercial hosting space. That will then determine if you by domain from wordpress.com or if you go to another provider such as tsohost.
Yes, you need hosting space as well as a domain name. Are you wanting to get involved in writing code? If not the. A photo blog - http://en.blog.wordpress.com/2012/05/14/photo-blogging-101-part-1/ - may be something to read about. Or you may just want a gallery. Have a look around the web for sites you like, then try to find out how they are created - such as looking for a Powered By logo, or looking at the View Source (so the code the browser reads) which may well contain some text saying what software is being used such as Wordpress, Jomala, or something else.
Email server is domain linked, though sometimes you do not get it by default. So if you want email via the domain, check that it is included and not an added extra.
Wordpress.com is quite useful for this sort of thing, their domain names are a little pricy but not too bad and they do it all for you and have lots of wordpress themes (the templates) which you can change at the touch of a few buttons. Have a look, create a free site (so no domain name) and have a play. If you like it, you can then upgrade to a domain name and remove ads. There are some limitations, one is that you can not sell anything from the site - no linking to affiliate schemes. However it does not sound as though you need that... or are you looking to sell the pictures?
No-one's hosting my anything, to be honest..... That's why I'm confused. I'm starting up a project, the website needs to have loads of photos of objects and art works, some contact details and maybe a mail feature.
Do I need to buy a 'hosting' package and how big do I need it?