protozo, sounds like you're pretty new to all this so I'll write up a quick guide for you on how to get everything up and running.
1. On your 3.15 PS3 first update it to 3.55 OFW. Sony is no longer keeping these archived so it may be somewhat difficult to find this. If you are unable to you can PM me for it, and I'll get it to you. Just for your own safety you can confirm the md5 of the update pup to make sure it's legit.
2. Once you've updated to that, you'll now what to install your CFW to jailbreak your system. Someone has already mentioned Geohot's, but personally I like rebug. Truthfully Rebug may be a bit much for beginners so I'd suggest Kmeaw's CFW for you. It has peek-and-poke that's compatible with all Backup Managers, and it just overall very stable and robust. You really can't go wrong with this one.
3. After you find Kmeaw's CFW install it, and that's pretty much it. You've now got a jailbroken PS3 that can run homebrew and games via a Backup Manager.
If there's other sorts of functions you're looking out of a jailbroken PS3 ask here, and I'll do my best to answer. This topic could go on for several pages, but this is the most very basic info for you to get started. Good luck!