[Galaxy S I9000 Q&A, Help & Troubleshooting] Cordial Humanoid:
Thanks a lot both to Soryuu and to compacity, I followed your instructions and they worked on the first attempt, so now my phone is rooted.

For the benefit of others, below is a detailed list of what I did. Steps 4 and 9 are just precautions/doublechecks, the rest are part of the actual rooting process, and basically correspond to Chainfire's "Instructions (long)" in post 3 of this thread.

My steps for rooting my phone:

I downloaded the ZIP file with the kernel from Soryuu's link, and extracted the .tar file out from the ZIP.

I downloaded a version of Odin: I checked Chainfire's descriptions in this thread, and found that the version of Odin compatible with the Galaxy S1 i9000 is Odin version 1.83 (newer versions are apparently not compatible with i9000 anymore), so I downoaded version 1.83 from the link in that thread.

I checked that my phone can enter download mode, using the instructions here. I did not yet flash anything at this stage, instead I just rebooted the phone.

I backed up my data. I manually wrote down notes that I had entered in the stock "Memo" app, I synced e.g. my calendar to Google, and I backed up the data in some of my downloaded apps to files on the , using their own backup features. I also wrote down my phone info like the info in my original post, my IMEI number, and so on: basically everything I can see in "System settings/About phone", "System settings/About phone/Status", and from typing *#1234# on the keypad; also anything in "Mobile network settings" in case there are some operator settings I would not remember. Lastly, I USB-connected my phone to my computer and copied all the backup files, and also things like camera files (DCIM directory) to the computer.

I disconnected the phone from the computer and turned it off.

I started the Odin version I had downloaded, called "Odin3 v1.83.exe" (I ran it as administrator, just in case it needed administrator permissions for something). In the Odin interface I clicked the "PDA" button, then selected the .tar file I had downloaded. I then looked at the "Re-Partition" checkbox to make sure it was not activated.

I put my phone into download mode, and then USB-connected it to the computer. Windows took some time to install some drivers. After Windows was done installing its drivers, I clicked the "Start" button in Odin.

Odin performed some operations, and the messages in the Odin window reported success. My phone rebooted at the end, I waited for the reboot to complete.

After the phone had rebooted, I checked to see that it now had "CWM" (CWM Manager v2.0) and "Superuser" apps installed. The CWM app reported that I was currently running kernel "CF-Root 4.3" as desired.

Now that my phone is rooted, I could next proceed to upgrading the operating system by flashing a ROM. A few questions about that:

I would also like to ask your recommendation: what is a good ROM to upgrade to? I am not looking for the latest features, mostly I hope to achieve better speed and responsiveness for the phone, especially considering the limited memory in Galaxy S1. Is it worth going to Ice Cream Sandwich or Jelly Bean based ROMs, or should I stay with Gingerbread ROMs, or even stay with the stock ROM?

If I flash a new ROM and dislike it after all, can I go back to the ROM I started from if I have made a backup with CWM, simply by restoring that backup? Or would I need to download a Samsung stock ROM from somewhere and flash that?

Thanks again for any help!