I have never gone straight from non rooted to custom rom.
Its better to first install cf-root kernel, which will root your existing rom, all data stays intact, settings, contacts etc.
Then install something likw CWM recovery, at this point you will then probably never need to use odin again unless you really mess up.
After CWM installed do whats known as a nandroid backup, this is basically a full backup of the rom on your phone, including kernel, modem, data etc. Whats not backed up is whats on the internal and external sdcard storage (reason is that stays intact in between wipes etc.).
At this point only then I would consider putting on a custom rom. As you now have a backup you can restore back to the shipped rom on the phone.
Be aware most custom roms I have used if not all of them are buggy, some bugs may be tolerable others may be severe. If you want a unbuggy root then just use cf-root on existing rom.
AOSP based roms like cyanogenmod tend to be very fast but also things like the camera tend to crash and the battery life gets very bad compared to touchwiz.
Omnirom has my eye currently, but its still been developed.
eg. currently I am diagnosing 5GHZ wireless issues which Qas* is aware of, I am likely to do a nandroid backup soon and restore my shipped rom to diagnose if thats an issue with the software setup or not. I am actually considering going back to my shipped rom permanently and just having that rooted since so many custom roms the dev's will say things like "tweaked" "optimised" without stating what they have specifically done and these tweaks may be causing other issues.
Some other things to be aware off.
Android 4.2+ the storage paths changed to support multi user, if you go from android 4.1 or older to 4.2+ the OS should auto handle the change, but if you then downgrade again you will need to manually fix the paths.
The newest modem drivers change the EFS layout, meaning unless you backup the old modem, once you have upgraded you cannot downgrade again. Dont assume you wont want to downgrade because there is many instances of people trying new roms and not liking them so going back, even the official 4.3 S3 rom is a mess to the point theregister did a news story on it.