I use
Namecheap. Been happy with them so far. I've also heard really good things about
Blue Host. Both are cPanel-based hosts at their cheap levels and both handle registration.
As far as the domain name itself , I'd grab a .com, .net and .org of something. As silly as it sounds, people tend assume .com for everything if they can't remember. You want the other two to forward to your actual space, even if you don't use the .com as your main space. It doesn't have to be your last name (mine, for example, is way too common), but you want it to be tasteful and easy to spell/say and remember (short).
BTW, coders don't usually have portfolios. Most people doing the hiring want to see how you approach solving a problem and how quickly you think on your feet. You're going to have to answer some technical questions from them as well. Getting a professional presence website
is a good idea, so I'd suggest focusing on that aspect more than uploading code snippets.