I use register.com for my domains: http://www.register.com/product/hosting_details.rcmx because I've used it before and know it's reputable, etc.

There are various costs depending on what options you buy, etc. It's the hosting that costs the money, not really the name. The name is a one-time charge per year usually or places might throw it in if you use them to host it, etc.

You can get a name from any of the places and the name is "yours" and then you can have anyone host it but it's easiest if you get the name and host the same place, otherwise you can get all tangled up with server name transfer and just hope you understand what's going on. I've bought names and then hosted them later somewhere else or not liked a host's software (control panel) and transfered the host and that's a pain.

Beware too, some places sell subdomains instead of whole domains so you have to use a portion of their name (kind of like the blogs here at psychcentral? I'm perna.psychcentral.com, for example) that's a subdomain, psychcentral is the domain. So if you use another place (Go Daddy, say) make sure the name is registered to you and there aren't any "liens" on it by the person selling it to you, etc. (like you must host with them or the cost goes up etc.). There's all kinds of hidden stuff that can happen. I'm sure Register isn't the cheapest but it "works" for me. They have nice, relatively easy controls, have free template stuff if you don't want to do the web page design, etc.