It all depends on how they contact us.
If we get a clear recognizable message, it's likely to be some kind of broad spectrum "Hello", designed to be interpreted as such.
It could be simply us picking up something like their GPS signal or communications signal.
Or we could pick up a bunch of coordinates and some kind of message, which is either an invitation or a warning to stay away.
I suspect that about a quarter of the population will be excited, another quarter will be terrified out of their mind, another quarter will call it a hoax and the last quarter will simply shrug and carry on.
If it's a signal, chances are it came a long way away and any response we may send will take anything from decades to millions of years to get there. Interstellar communication at the speed of light is incredibly slow by human standards.
We'd be doomed to figure out a response and then have to wait ages to get a reply. Communication with other stars may take aeons.
First of all, there is no point in staying quiet, even if we decide to stop emitting any signal (which includes our GPS satellite system) our existing signals would give us away for a very long time.
There are several options for the Aliens.
They are not an immediate threat, probably stuck in their corner of space just like us.
They are a type II civilisation and may have the resources to send someone or something, but this may take ages.
They are a type II civilisation and are not interested in dealing with outsiders for whatever reason.
They are a type II civilisation and we get the "tough luck guys, we claim this galaxy." followed shortly by a Nicol-Dyson beam or they sent a fleet of killer ISBM's or relativistic kinetic projectiles or drones. We're essentially dead within a few years of getting the message.
More room, resources etc are unlikely goals for aliens to come and visit us. There should be enough room in the average solar system to house trillions with elbow room to spare and I'd be surprised that we'd find two civilisations contiguous to each other, so there would be more than enough solar systems in between us and them to make a trip all the way to our planet to simply mine whatever they are looking for a bit odd, since as far as we can ascertain our system should have nothing unusual to offer that you can't get elsewhere in the galaxy.
Dyson spheres or swarms are not that hard to achieve, they are probably less labour intensive than trying to expand onto other star systems and can satisfy almost every demand of an advanced civilisation quite effectively without having to travel massive distances and spending eons doing it.
What about FTL travel you ask ?
It cannot be ruled out, but our current understanding of FTL is pretty much.
- Concept
- ???
- Warp five mr Sulu
There are a few hypothetical models and some maths that don't preclude FTL per se, but practical applications might be out of our reach no matter how much money we throw at it.
Traveling at relativistic speeds is horribly slow by human standards, but once you reach a certain technology level the human factor becomes the glaring weak spot and all your philosophical hindrances don't weigh up against the benefits of altering people to live on an "interstellar timescale" Once you do shift timescales FTL becomes a moot point.
Visiting Aliens
I doubt they would come to conquer us, unless they have some philosophical reason to do so. If they can come all the way to us, we're 
ed.
They come to harvest our resources
What could we possibly have that they should not be able to get in their own system. The only reason would be close proximity and they are simply moving onto the next system to get more resources. They would probably not skip other systems to get to us first, unless again they have really weird philosophical motivations.
They come to harvest us
That problem can be solved in a matter of hours. Take a large enough sample of humans, Swab the inside of the mouth of a few times and you can clone humans at leisure for whatever reason you may have. That gives you a near unlimited supply of humans.
They are explorers and simply wish to talk to us
It probably wouldn't be the USS Alienprise, it's either going to be a massive ship or a fleet of ships with all the resources to explore our world in every possible detail. Most likely they would figure that specific protocols would have to be established to ensure that there is no risk of contamination and that they don't accidentally damage our most precious artifacts. They would probably need years or even decades to find ways to communicate effectively and find methods to translate all our media and copy it onto their computer systems.
They might even offer our scientists a return trip. "Build modules suitable for humans and all their equipment and here are the specifics for how to connect them to our ships for the trip of several lifetimes."
Our own reaction might vary to other degrees.
We do have protocols for dealing with an alien message.
It's unlikely that any single nation might pick up the signal and be able to keep it a secret. Similarly the odds that the UN can keep this under their hat is small because the odds of anybody independent discovering the signal and going public only goes up with time.
The major hurdles would be individual reaction, political and philosophical/theological.
I can see certain religions reject the claim of contact with another civilisation outright. "If it's not in the holy books, it's a lie." type mentality.
Politicians might get upset and try to cover it up for fear of panic or possible other implications. Unlikely, but I can see some countries declare it a hoax purely to make a political statement. Also see denial as a political tool to crank up the problem of "fake news" to disrupt society.
We might get some measure of panic in certain populations, individuals might decide it's time to flee to the hills.
Even more likely is the "Aliens-Shmaliens !" attitude of many people. "It's all scientists trying to get more funding" type reasoning.
I doubt that the planet will go collectively nuts, most people will remain dubious and skeptical at best and without any real interaction it's probably going to fade away from daily life. If we get something like radio communication or even TV signals we might have a treasure trove of alien culture to listen and watch and try to interpret.
From outer space I mean …
