Congrats and good luck! My first time went smoothly and my app did not get rejected surprisingly. Usually it takes a week or maybe less depending on the workday it's submitted on. Just be calm and patient, and it should pan out nicely
I submitted my first app to Apple just after midnight on a Thursday/Friday (the 23rd/24th of June.) I was notified a week later, on the morning of Friday the 31st, that my app was in review. That night, ten hours later, I was told it was being processed for the App Store, and then seconds later was told it was available for sale. I started sending out links to friends, some weren't able to initially use the links and got back error messages from the App Store, but by Saturday morning all the links seemed to be working.
So, yeah, that's possibly more details than you were looking for on my sole experience with Apple's App review process.