I am not any kind of expert, but will try to offer some helpful advice. 🙂
As said above, you are likely to have some free space available through your ISP. That would do you if you just need a little bit of space and don’t need to run applications to do things on the server.
One problem is that you will be stuck with your ISPs ‘user space’ as part of your web address.
So if you are unfortunate enough to use BT as I do… it would be something like:
http://www.mywebsite.btopenworld.co.uk
If you want to have your own web address and some space from a host, then you essentially have to pay for the two different services, but you can often pay the same company to do it for you so you don’t have to worry too much about the details.
I use hosthere.co.uk
I have to pay them every two years to renew the www. co.uk address, and then yearly for the webspace I want. You can decide how much storage space and how much bandwidth you want to pay for.
There are many other companies who do exactly the same as the one I use. They have always been helpful when I needed advice so I have stuck with them.
I hope that helps a bit.
I am VERY basic with this kind of thing, but hope my explanation makes it easy for someone else new to it to get the hang of things. 🙂