I'm not sure about the OTA updates, but my root took about a minute, and I used the galaxy S one click root. A quick search around here should net you a download, and once you have it, make sure you have the samsung drivers installed on your computer.
Go to settings: Applications: Developement- and enable USB debugging. Now plug your phone in to your computer, open the zip file and click galaxy_one-click_root.exe. It will open a small screen with two options: "one-click Root" and "one-click UnRoot". Click "one click root" and it will connect to your phone and install "update.zip" to the internal sd. You will be given a command prompt window with instructions on how to proceed.
I just did all of this yesterday, for the first time ever even attempting to modify a device. It was very easy, and I am less hesitant to keep moving forward after rooting and flashing a few different ROMs to my device. If you do this, I suggest once you are rooted to download ROM Manager from the market, and create a backup of everything, so in the event something goes wrong, you can flash back to just after you rooted, use the one click UnRoot, and you are back to stock. From what I am to understand you will be hard pressed to brick your phone to the point you can't recover it somehow.
