I only do basic custom websites for small businesses. A basic site may include information pages, a contact form, blogging features, and photo galleries, wrapped into the website's look and feel.
Free tip: Don't go overboard with your website!
Many businesses get sold on a complicated website that doesn't do anything for them. In this day and age, a small business website should portray your company's image, be user-friendly and meet your marketing goals while being as simple as possible.
web hosting and domain names
These are places I like and recommend:
Domain Names at NameCheap. I know you've seen GoDaddy everywhere. I don't recommend them, and you can find a lot of people who don't like them for various reasons. One reason is, they try to sell you a bunch of stuff you probably don't need, and nickel-and-dime you for features that are standard at most places.
That's why I moved all my domains to NameCheap. They have competitive prices for domains, and better prices than GoDaddy for basic SSL certificates ($10.95 RapidSSL for 1 year). No place is flawless, but NameCheap is very good and has monthly discount codes for new domains. Another good alternative that people seem to like is Moniker.
A good web host is also important.
For general hosting, I like InMotionHosting. If you are hosting a WordPress site, I recommend WPWebHost. There are plenty of hosts out there. I have experience with both of these companies, and I still like them.
Ones that I don't have recent experience with but seem to have good feedback are BlueHost and HostGator. I'm hesitant to endorse just anyone, but these guys seem good.
If you want to keep all your eggs in one basket, domain registrars will often offer hosting, and web hosts will often times give you a deal on domain registration as well. I prefer to diversify as much as reasonably possible and pick the best companies for each.
Note: Domain and web hosting info is updated as of 2020. The links above are affiliate links, and using them will give me a kickback if you decide to do business with them. Thanks!