A long, long time ago, someone here suggested www.8-95.com as a webhosting service. I have used them with no problems that I know of.
They now have a “free” hosting service – you have to pay US$15/year to register a domain through them, and then you get “free” hosting through them for that year. It is a very limited package, but it might suit a very simple, low-traffic site. If you overrun your limits, you can upgrade to their “non-free” hosting for $18/year (cheapest) on up.
I’m using the scare-quotes around “free” and “non-free” because, obviously, US$15/year for registration is considerably more than the US$8/year retail that GoDaddy charges (and I’m sure it’s lower in bulk, which is probably what 8-95 is doing). Still, it’s not a bad deal, and they have done ok by me. They don’t do support, though – if you have a problem, they have a “user community” board that you can post a note on, and you’ll just have to hope someone else knows how to do whatever it is, and wants to help you out. The people who post there are genuinely friendly and reasonably clueful, but they don’t have all the answers.
BTW, I don’t know if the “free” hosting includes ads or not. I don’t think so, but you’d best read the contract carefully and maybe email them to ask. If they’re going to stick popups on it or anything, you can always go with the US$18/year package (assuming it suits your needs), and register through a cheap place – total of about US$27/year.
As far as building a site, the easiest way to do it is to find one you like which is similar to what you need, and then copy all the HTML. For graphics, there are plenty of icons available in the public domain; if you need something special, you’ll have to find an artist to do them for you, of course.