I'll have a go at this one.
First off... If you want the domain name you had/have with CWI Hosting, press them until they give it to you.
I use godaddy to register domains and host them at pair.com. Never had any problems with them.
What you need to watch out for is what happened with CWI Hosting. With godaddy you really will own your domain name. Godaddy will try to sell you a lot of stuff while your registering your domain. That's how they have such low prices. Just keep on clicking on the "no thanks" and move on to the next page. You can host with Godaddy but I never bothered reading their ads. Probably not the best place to host.
I've been with pair for about four years and my sites have never been down (that I am aware of). With your host you need to watch out for that. How fast your site downloads is another thing. A hosting company may try to get business by not charging much for bandwidth which can slow down their servers.
First register with godaddy. Say you just want to park the domain there. Open another window and go to pair. Get their $5.95 plan which includes hosting for one domain and any others for 1 buck each. You can always upgrade to get more space and bandwidth later. Go ahead and pay for 12 months to get the discount. Tell them you already registered the domain. They will give you two nameservers, a primary and secondary one. They look something like this: ns284.pair.com, ns0000.ns0.com. Go back to godaddy and give them the nameservers.
Pair will help you with the whole process.
You can change your registrar any time you want.
If the registrar goes out of business, the domain is still yours. Don't know any details.