Welcome!
Homebrewing is incredibly fun and is a great "companion" hobby to BBQ. I actually got into BBQ 2nd, after homebrewing for about 10 yrs.
One great place to start is:
http://www.howtobrew.com
This is John Palmer's online version of his book. It is the 1st edition, so the later print editions are updated and hold much more information. That said, this free online version is jam packed with great info and you will not go wrong using it.
Having a local home brew store (commonly called LHBS in the homebrewing forums) is key. Yes, you will be able to find stuff cheaper online, but the ability to go pick up a last minute ingredient or keg part is crucial. Keeping the LHBS guys in business is a must. They are usually very helpful, too.
check out
http://www.northernbrewer.com,
http://www.morebeer.com,
http://www.midwestsupplies.com
for ideas. You can find a good starter kit for between 75 and 100 bucks. Don't cheap out on something like Mr. Beer. By the time you are getting good beer out of it, you will have outgrown it and will then be out looking for a good 5 gallon setup, which is just as easy to use.
Blue Moon and Shock Top are variants of a style called "Belgian Witbier". It is a fairly easy style to brew at home, as you can use pilsner extract, wheat extract, a small amount of hops (usually Saaz or Hallertaur), and a Belgian yeast.
It is on the lighter end of the spectrum (ie, lower alcohol, color and alcohol content are NOT CORRELATED), so it will ferment rather quickly and be ready to drink in roughly 5 weeks.
In the meantime, try some Hoegaarten, Alaskan White, Celis Wit, Bell's Winter White, or Allagash White. All are better versions of the style.
BTW, you will NOT be able to brew BudMillerCoors right off the bat. They are actually some of the hardest beers to brew. Besides, why bother?
HTH-