Having your own server normally indicates having the web site hosted on your own computer which is within your own business or your own house.
But most people host their web site with a separate hosting company.
So when you say a server do you mean a company to host your web site?
If your web site is going to be pretty basic (no complex databases or ecommerce) then go for a cheap "home" package or small business package.
This should be pretty cheap, and you can always upgrade it in the future if your needs expand.
I have one of my sites hosted with Netcetera, and they do a basic package for �25 a year.
http://www.netcetera.co.uk/Hosting/lite/
I am not saying Netcetera are the best, just using them as an exmaple, there are loads and loads of hosting companies.