Super economy is just a fare type (cheapest you can get if available). It doesn't say anything about the travel class - you can have a super economy normal seat, a berth in a 6-pax couchette, or even your private compartment! (I believe this starts at 69 EUR one way, if I remember correctly from my last Catania to Rome journey).
While the terms might be confusing (indeed, check seat61.com and their excellent summary what is what, and step by step help with booking) it is actually quite straightforward. Check the options of travel, and then see if there are cheap super eco or economy tickets available!
Italian overnight trains do have a bad rep at some corners of the internet, but this is vastly exaggerated/talked by people who have taken a train decades back. To me, certainly if you can snatch a private compartment (which you can lock from the inside) in advance, it's just a great great deal for that money! Even in shared couchettes its perfectly safe, as other passengers add to security. Just take normal precautions (eg. dont leave a small bag completely unattended in full view close to the door for someone to snatch it easily) and it's all fine really.