Gotta agree with Dreamhost first and foremost as a domain registrar. If you search back past Slashdots, you'll see folks have chimed in to say how simply searching and pricing your desirable domain name at a lot of registrars, effectively and immediately places your desirable domain name on other people's (or the registrar's) radar. In other words, it is not kept private for you, and if you delay much at all, you'll probably see someone else (like the registrar themselves) might very well snatch it up, so you'll at least have to pay more. I can vouch this doesn't happen with Dreamhost (I've tested it myself, along with the other registrars folks had mentioned, and saw those results too). Domain name searches at Dreamhost remain private. GoDaddy was one of the abusing registrars I am referring to, if I recall correctly. I've had assets on Dreamhost now for 10 years, this coming summer.
Also, if your website needs are as simple as you have written of, then dreamhost is an absolutely fine host. Their customer service is very good, prompt, and helpful too. A very good deal for the price, if your website needs are so simple.
That being said, I can tell you the cheapest level at Dreamhost is not suitable for a heavy CMS like Drupal. If you are running something like Drupal, then you should really buy the whole VPS. Dreamhost has invested heavily in their VPS options in the years since I was seriously trying to get Drupal to work over there, but I find Linode.com and digitalocean.com VPS options to be very good for the task. Also, just so you know, my recommendation for Linode and Digital ocean is based on my own rather heavy server installations and configurations.
Finally, domain names are like wo/men. All the desirable ones are already taken.