Well, with time you can suspect presence of stuff in a system. Here is a couple of hints:
-If you find probes, there will probably not be anything else than probe and survey ship most of the time, and you can estimate where they will be (ring, planet, sun, and asteroid cluster)
-Kind of obvious, but if you find ship (whose discovery grant you xp), there will probably be other stuffs like stations and abandonned planet. A quick way to know that is the presence of gates and arrays
-Know your colors: yellow, white and blue system seems to have better chances to get abandonned stations and the like. Red small stars are mostly barren or with probes but sometimes get a few interesting loot. Nebula are rarely interesting but do get the rare research station. Black hole (alone) and neutron star are dangerous but have great loot most of the time.
-Still, as it is random, you can always miss something, or found nothing in supposed to be great systems.
As a way to go, I explore systems next to the core without missions. I use analyse mission to get to interesting place, and plan ahead to have fuel and space to visit everything on my way. Try stellar system with a name, I think they have a better chance to yield something interesting.
Please note that it is still exploration, and all that stuff is only a rule of thumbs