Take the Good Eats episode with a grain of salt. While I think one could make perfectly fine beer the way Alton Brown did, I don't think one could make great beer that way. Especially if you want to make Belgians.
One thing though is beer making isn't as hard as it looks. Here are a couple of links
(THE POSTS ARE FINE BUT THE SITE IS NSFW DUE TO THE BANNER ADS AND AVATARS). However it is a pretty good nutshell opinion of brewing IMHO.
• View topic - Beerntits Home Brewing Guide Pt 1
• View topic - Beerntits Home Brewing Guide Pt. 2
The second link deals mostly with equipment. Good basic equipment kits like you linked to are fine. As you explore other techniques, you can add or upgrade equipment as you go along. Check to see if you have a local home brew store. You can often get better deals as well as personalized help from the shop owners. I have a LHBS an hour away from me and rarely buy on-line as I like shopping for my beer toys in a brick and mortar place. They do have a website.
High Gravity Homebrew & Winemaking Supplies
This is the kit I started with:
Beer Equipment Kit - Two Stage - Equipment Kits - High Gravity I now brew all grain, but still adhere to the home brewer's mantra RDWHAHB. Relax, don't worry, have a home brew.