All good hosts will allow you to host a site with any domain suffix you like. I have all kinds of domains, including .co.uk, .com, .net and .info and I have hosted them with all sorts of hosts, from Web-Mania, 1&1, 2020 Media and Easily, to name just a few.
Select the domain name and suffix you want, register it and host it. Most good hosts will allow you to do this under the one roof.
1&1 are about the least expensive for registering the domain. You may find far cheaper hosting with another provider though, and the 1&1 control panel allows simple DNS management so you can point a domain registered through them to any web host you like.