It all starts with your domain. Do you fancy a .com or a .co.uk?
There are also other options, such as .uk, .biz and many more, but the most common are the com or co.uk. Usually, your domain is your business name, but it can be whatever you want it to be!
You can shop around for your own domain or I can do this for you. Some companies offer great start up deals, with domains from a mere pound for the first year, so it's always good to do your research before committing. Again, I'm more than happy to do this for you if you prefer, and I will never add on any extra fees. The domain is registered under your details and the invoice will be generated directly to you for payment, via the domain company.
The same applies for hosting. Hosting is basically the space in which your website resides, and is usually 'rented' monthly or annually for a fee. Obviously it all depends on the size of your site (as well as other factors) but hosting fees can start from around £12 per month, with reductions on that if paid annually. The addition of a webstore, bookings system, and other more complex features will make it more expensive, but this is an essential expenditure if your business requires it.
As before, the hosting is registered under your details and payments are made by yourself directly.