First priority: get it updated to official Jelly Bean (4.1.x). Since you're rooted, you can't get it by checking for updates on the phone, so just do it via Odin. You need a PC with appropriate drivers installed, of course. Follow this guide, but get the official firmware for your region from SamMobile instead. Let the official ROM boot once before you proceed.
Keep a copy of the CM ROM you're about to flash either in internal storage or in a microSD card inserted in the device. The latter is preferred.
After that you're clear to read CM's official installation guide here, but instead of using Heimdall, keep using Odin which you used in the last step. Replace official firmware with this in the PDA/AP slot, leave other slots empty and start flashing. As the flashing comes to its end, quickly hold VOLUME +, HOME and POWER to boot right into recovery mode.
From there, use VOLUME keys for navigating in menu and HOME/POWER for confirmation. Choose
wipe data / factory reset then choose
install zip and select the location where you've put the ROM at. Select the ROM to start flashing. When done, do not immediately reboot, but instead install IsoRec TWRP recovery by following this guide, or else you'll have no usable recovery after boot.
Reboot system now after that.
I know it's quite a mouthful for you to handle right now - do it step by step, report each error and choke points, and in case anything goes wrong, the first step (Odin + official firmware) should always reset things back to beginning.
To other members: although I had much experience flashing Samsung phones and Android devices in general, I don't own this particular device, so feel free to edit and correct faults if you have sufficient backing.