If all you need is root access, try flashing the Siyah kernel via ODIN. Ensure you get the S2 version, as the dev has one for the S3 as well. Also, you will need the TAR version as you will flash it via ODIN (at least for the first time). Later instances, you can get the ZIP format and flash it via CWM (ClockworkMod recovery, which is built into the kernel). Apart from features like more processor steps, you can also overclock/underclock, adjust various parameters and have features like Backlight Notifications.
Since you will flash this kernel, you DO NOT need to flash the firmware. You can keep the stock firmware and your data intact. This kernel automatically installs root access so your primary requirement is also fulfilled.
As with all operations, ensure you have an off-site backup of all your data.
As an aside, once you install the kernel, get the ExTweaks app from the market which is designed especially for this kernel and offers a GUI/frontend to access many under-the-hood features.
Assuming you have all the drivers installed, here's how you go about it:
Download the TAR file of the Siyah kernel. Note that the latest series is for ICS, in case you're running Gingerbread, search for and download the appropriate older version of the kernel.
Start ODIN and connect your phone via the USB cable AFTER you enter DOWNLOAD MODE (Press Vol down + HOME + POWER button simultaneously for a few seconds after completely shutting down phone. At the warning screen hit Vol UP to confirm entry to download mode).
Once connected, you should see a COM port number with a yellow background.
In the ODIN program, press the PDA button and point to the TAR file.
make sure ONLY Auto-reboot is ticked and then click START.
If all goes well, you should see a green box with PASS! shown after which your phone will boot up. It may take a minute or two, so don't panic.
Refer to the FAQ and the respective threads on XDA-Forums for more info.