Thanks AlbertP, much appreciated. Now I'm confronted with another problem.
I've created a larger swap partition. Although not 3 gb but 2,5 gb - I didn't find a way to merge partitons so I deleted one unnecessary (or rather, eh, unknow) partition and formatted it as swap... and then googled how to include it in etc/fstab. Anyhow, the suspend option doesn't do anything else than to blacken the screen and - I can't tell for sure, but I guess - shuts down the hard drive.The psu fan, for example, runs as normal and the computer is as noisy as in use. If I were to hibernate it shuts the computer down completely and it will only react to the actual on/off button on the computer case, and when pressed, it will do a normal/full start up.
So suspend does "too little" and hibernate "too much", if you understand what I mean. Can I fix this? I'd like to hibernate in the sense that computer is shut down but will resume to where I was before hibernating.