So why would they be looking? I can think of 3 primary reasons for them to look. Firstly, they are enlightened creatures looking to expand their knowledge of the universe, and are looking for other life. In which case they are likely to be peaceful, and would be a benefit to us (hopefully they'd quash religion at least). The second option is that they are looking to conquer, but that then leads to why? Why come across the deeps of space to attack a race that has barely made it into orbit? Either this race would need to be ultra-aggressive bordering on genocidal psychosis, or they know something that we don't about us and for some reason fear us.
So that leaves option 3, colonisation. This for me is the most likely scenario, that the race is looking for places to settle upon, ones that already contain life. Whether this is because their home has been destroyed / rendered uninhabitable, or whether they are an expansionist race, the fact is that they would arrive, likely with superior technology (although maybe not in all areas) and find us here. So that begs the question, what do they do next? How desperate are they to find somewhere to live? And could we stop them if they decided that force was the only option to them?
You think that colonization is the most likely scenario?
1: Earth is too small for any alien race to colonize. I think that within thousands of years of breeding ( for species that use sexual reproduction ) or multiplying ( asexual species ), there will be nonillions of them. Earth can only comfortably fit about 4.5 billion humans. Instead of thinking about aliens colonizing planets or moons, think about quadrillions of floating cities ( each the size of a red giant star ) floating in trillions of nebulas; or maybe even gigantic ringworlds surrounding every star in the galaxy.
2: Earth likely is no match for the alien's home planet or moon. Other habitable planets and moons are likely radically different from Earth. As a cross-example, Europa is 100% habitable. Certain deep sea animals could live in Europa's depths.
But would we colonize Europa? No, it is too radically different from Earth, we would get lethal doses of radiation.