welcome to JavaRanch. great choice on new skill.
I, like you, came from the Web Development field before entering Java. I had been designing sites for about two years. Programming experience was limited to a month of trying Visual Basic (I hated it)
I wanted to start studying for the exam right off the bat too, but before studying you have to learn it. I recommend picking up Thinking in Java like Jose said, but don't limit yourself to just one book. Heck no.
Go get Sams Java in 21 days, Beginning Java 2, and the Complete Guide to Java 2 Certification(which on this site we refer to it as the RHE)
This should take you from two months, to however long you want to learn it. It can be quite facsinating. Then move on to a more advanced book like A Programmer's guide to Java Certification (Mughal's Book)
After you get you hands dirty with that, then start studying for the test. Pick up an Exam Cram by Bill Brogden.(if you can find one. The company that makes them went out of business) Also, invest about $18 i think in a JQ+ mock test software. I haven't used one, because lack of funds (ok im dirt poor) but I hear they are the way to go. I wish I had one. Most people here will sing its praises. Don't forget the mock exams in all of the books you pick up.
Then just take free mock tests up the ying yang until you take the real exam. Free mock tests that I personally recommend is Jxam, Mughal's mock, the 3 Marcus Green mocks, and of course, Val's Mock. (don't be mad if you do bad on JQ+ or Val's mock. JQ+ is harder than real exam, and Val is like a human compiler.
Much Respect Val)
Anyways, to make a long story longer, the road to the SCJP cert can be very tough. But if you can stick with it, and don't give up, you'll make it.
Oh, and of course your road will go much more smoothly if you use this site. You won't find another site anywhere like it. The people are helpful, we are all looking to know more, and Java Ranchers stick together! (applaud now!)
Hope my babbling helped,
P.S.> JavaRanch! Pray to the Java Gods! I take SCJP test tuesday the 21st! Burn some Microsoft book to appease the Sun Java Gods! lol