First off, if this is really business critical, you should hire a professional, period. That being said, if you want to try it yourself, here are some answers to your questions:
(1) Any version of Linux will work fine. For a server, I like a version that is going to be supported for a long time (read not Fedora). I personally like Debian testing on servers, but Slackware would be a good choice, or even FreeBSD even though it's not Linux. For something very newbie friendly, you might want to invest in or do an FTP install of SuSE professional edition or a RHEL clone like Whitebox. Heck, you might even want to spring for RHEL, if you want support. This comes down to what you feel comfortable with and what your budget is.
(2) Pretty much any mainstream server hardware will work well with Linux. I've run it on both dual Athlon MP and dual Xeon rigs and never had a problem. Dual Opterons make for a sweet set up now. Dual CPUs w/ 1-2 GB of RAM is way more than you need to host 7-8 medium-traffic Web sites. In fact, you don't need any more than that unless you're planning for huge amounts of traffic or your going to be setting up a complicated Web services or CORBA infrastructure, which is not for the uninitiated.
(3) When you install the server, install the Apache, PHP, and MySQL . When you register your domain(s), you'll be given an opportunity to provide authoratative name servers for them. You probably aren't going to be runniung your own DNS, so pick a free service like zoneedit. Simply use it to point www.domain.com
to the IP address of your Web server (you do have a static puclic IP address for this, I hope). Then configure name based virtual hosting in Apache to load the correct page based on the request. This is a bit complicated, so Google on name based virtual hosting and read up on it.