Domains are simple. Just register your domain at a place like MojoHost. Unless you purchase a premium domain, then your domain should only cost around $10 per year or a little more.
You should definitely sign up for privacy options, if they are available, but that is all you need. When you sign up at places like GoDaddy, they try to sell you all these extra services you don’t need. Don’t fall for it. And no, you don’t need to pay people to submit your site to Google. Google WILL find your website, you better believe that.
The number one rule of domains and hosting is NEVER have your domain and your host on the same company. So if you’re hosting with company A, then buy your domain from company B.
I use MojoHost for my domains and hosting, but they are an official domain reseller – plus their service is so good I can’t turn them down. I know that goes against my rule, but this is the only company I would use for both hosting AND domains.