if i'm to take my photography seriously, i should just go for Lightroom, and don't even look at Elements?
It depends on how you work. Lightroom is really
good at importing/managing your photo collection, and doing basic photo adjustments. Global adjustments such as contrast, saturation, etc. as well as things like cropping and rotating. For these global adjustments, no other software allows you to work as fast.
What Photoshop (Elements or Full) gives you is power. You can't do pixel level editing in Lightroom. There are no layers.
I think a good way to work is to have both. Most of your tweaking will be done in Lightroom, because the user interface is tailored to make the import->adjust->export workflow super fast. However, for shots where you either need more control, want to do pixel level editing, or want to be a bit more creative with your final composition, you would export to Photoshop.
Given that both have a free 30 day trial, I would just download them and play around, to decide what works best for you.