Why did they invite the humans to come visit, if they wanted to destroy us?
Who says we were invited? That's Shaw's interpretation, but the paintings could be something else: a warning, or maybe a copy of a glyph seen on the ships. It's not explained in the film; the map to the location and the giants is significant, but that's all we actually know.
Who says that they want to destroy us? Again that's the interpretation of the characters based on their contact with one (admittedly very aggressive) Engineer and the black goo. Janek refers to the black goo as an arsenal, but while it's obviously very dangerous that isn't necessarily its designed purpose.
At the start of the film we see an Engineer sacrifice himself using similar technology to the black goo in order to seed a world (possibly Earth) with his DNA. I think that indicates that the Engineers have uses for the technology beyond destruction and that they're quite prepared to destroy themselves in the process of using it.
At the beginning when Holloway and Shaw are showing the matching cave paintings they vary greatly in date:
Two are fairly recent: Mayan (620AD) and Hawaiian (680AD). This is interesting because earlier on they found the that the calamity that befell the Engineers on LV-223 happened about 2000 years ago - if Prometheus happens in 2093 the implication is that some of the cave paintings happened after the Engineers set up whatever they were doing with the black goo on LV-223.
I think the black goo is not intended to destroy humanity as such, though that may well be a side effect. I think (and this is pure conjecture) that, to the Engineers, whatever the black goo is supposed to do is some kind of step forward. If the painting are an invitation then it's to come and become something else.