OK, lots of responses here, from all kinds of people — mystics to Trekkies and back. Let’s have a look at some ideas.
FTL travel impossible, some say. Expensive and difficult, say others. Well now, in the 1700s, flight was impossible until the Montgolfier Brothers et al took to the air in balloons and by the 19th Century the dirigible airship was developed. Heavier-than-air powered flight was ‘impossible’, until the Wright Brothers did it in the 1900s and by 1947 the ‘impossible’ breaking of the sound barrier had been achieved. I could go on, but so many ‘impossible’ things have been achieved, one after the other, that really scientists in particular should stop using that word. In one respect, if in no other, Star Trek got it right — FTL travel will not be invented in a gleaming lab by men in white coats, but by a nutcase working in his garden shed. But it will be invented, if only because somebody said it was impossible, and that word will always be a challenge to somebody, somewhere.
Humans will go into space, if we survive long enough. Why? Because it’s there! We’re a nosy bunch.
Aliens. You do realise that we could walk right past the dominant species on an alien planet and not even recognise it as being alive? Any more than it might realise we are alive? For all we know, there could be another intelligent life-form and civilisation on Earth, native to Earth, that we don’t even realise is a life-form and which is equally ignorant of us!
There could be others who we recognise as life-forms but not as intelligent ones. This is a different situation in that the way two such species act toward each other will be unpredictable in its consequences. Each could end up thinking itself dominant over the other, for instance. Or one might exterminate the other, assuming it to be a pest of some description.
As to the races we recognise, and recognise us — probably due to a mutually-recognisable use of technology — there will be caution and suspicion on both sides. Historically it is our curiosity which has uncovered scientific principles, but our warlike nature that has turned them into technology. Because when we aren’t at war with each other, we’re at war with the environment. Clothes, fire, buildings, cooking, etc. all come from humans migrating out of the African climate we evolved in. We have no reason to suppose that a similar species’ experience has been any different. Little green and grey men might well have SF novels about big pink, brown and black men invading their planet! Intelligent reptiles might have myths of how valiant lizard knights save fair lizard maidens from voracious, fire-breathing, winged, furry monsters!
So on both sides there will be caution, suspicion, hostility, curiosity, fascination, hope and fear. There may be war, but there may also be peace, or we may just decide to leave one another alone. The Galaxy is a big place, after all.