Hosting
I provide temporary hosting during the development of your website which you will be able to access to see 'work in progress'.
For permanent hosting, I recommend that most clients go direct to the hosting company used here (my only connection is as a satisfied customer!) Signing up involves filling in an online form with your personal details and payment details, and then waiting for your account details to arrive by email.
The cost of hosting does vary with the amount of traffic your site generates, the features offered (up to date providers should offer PHP 5 and MySQL 5) and the level of support offered. For a small business the cost should be in tens of pounds per year, rather than hundreds - on the other hand if you find yourself having to upgrade in the future to more expensive packages it will be certainly due to increased revenue far offseting the cost of your site!
Domains
You will also need to register the 'address' or domain of your site e.g. myacewebsite.co.uk. You can do this via a number of companies - again I am happy to recommend to clients the company used here, or we can register it on your behalf. In the latter case I will ensure that ownership lies with you, the client.
Typical registration costs of domains are £3 per year for domains ending in .uk, and £9 per year for domains such as .com, .net or .org.