Hello and welcome. Your gonna have a blast. Find a local shop that can get you on a few bikes to see what you like, what fits and what works for your budget. I shopped around a lot before I got my cross bike. The more bikes you can ride the better. I went 2 cm smaller than the road size frame I would use. I couldn't find anything local that I could afford so I looked on ebay and Craig's list . I got really lucky and found a good used bike that was in my budget. Good luck and Happy muddin!
Oliver's got the hot ticket. There's a few local series where you can check out the action starting September 19. If you're going to be near Burbank on this Sunday morning, I invite you to check out a cyclocross clinic and ride at H&S Cycles. Here's the address:
509 N. Victory
Burbank, CA 91522
Get there at 8 and look for the crazy cross woman named Dot. She may even have a bike you can rent and get a feel for a cross rig on the cheap.
The H&S Clinic is tomorrow (9/5). There's a few more in the LA area, as well as OC and San Diego/San Luis Obispo. Dates and specific locations are on the schedule page of Socalcross.org - the site's getting updated soon so I'm not linking directly to the page in case they change it.
Also, for demos - they're usually available at races as well as clinics, but it's a really good idea to contact Dot (through the website) ahead of time to be sure they've got one reserved for you, particularly for races.
Screw the bike, Screw the advice, go out there & have fun!!!! If you like it then go for it, get the bike, get the gear, but if you are new, visit some training clinics, do some races & see what you think.