The approximate costs for getting a small website online are :

• Registration of a domain name - this varies depending on the provider but is usually around £10 - £20 and needs to be renewed annually.
• Hosting fee -  £50 annually.
• Building the site - this depends on how many pages you want and other variables but a simple site would be around £250.
• Updates and changes after the site is live -  £25 per hour.

I recommend registering your domain in your own name as this leaves you free to move easily to another website designer in the future should you wish to do so.  I am happy to offer advice on this. 
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I can offer a more detailed quote after our initial consultation.