Domain names are as important part of branding for any business or company. The .com is no longer the only option for a business. There is .net, .biz, and even .us. There are more, but for most small business clients, .com and .biz are good choices.
Domain name registration is handled by domain name registrars. You can use your business name, or a close version of it, keeping it as easy to remember as possible. Shorter domain names work better. There are many places to register that name, though one needs to read the agreements carefully. Some places charge for options that should be included in the deal, and that's why they can offer domain name registration at such a low introductory fee. Some pull you in using sales, but again, make sure to read the entire agreement. You should also make sure you know exactly what you are getting with your registration and what services you must pay additional fees to use.
I can recommend Hover for domain registration. I have been using them for years, a number of my clients use Hover, and we have always been very happy with their service. Check out Hover for yourself.
Web hosting is something we must all consider very carefully. Just like with anything else, web hosting plans and quality will vary; simply put some are better than others. Custom design clients have the option to host their site with me. Please ask about my website hosting price structure.
Some companies only offer shared hosting like iPage (you can see reviews here) which is a hassle when you need to upgrade to a higher plan. I offer a variety of plans that would fit your needs. Also, some offer a drag-and-drop website builder (eHost, for example) but nickel and dime you for what should be standard features.
Web hosting options for my clients.