Aka: What I am asking is: what are the basic elements a society capable of space travel needs? What key factors determine a species'capacity to become spacefaring and what cultural and societal aspects are required to become a spacefaring society?
The short answer: Whatever you want. We have no real-life experience with spacefaring civilizations, so we can't say for sure what needs to be done to get there.
The longer, more speculative answer:
Resources: A civilization that formed on Europa (probably) wouldn't have the raw materials needed to reach the Space Age, so they likely couldn't actually build a rocket even if they wanted to.
Biology: Kind of a looser restriction, but it would be a lot harder for a race of intelligent aquatic life to reach space, simply because they'd (probably) need to launch a lot of water to breathe in. The ability to breathe a gas is helpful in that regard.
Some measure of planet-wide peace: A constant state of war doesn't seem to lead to large-scale space travel. If you're always at war with someone, you don't want to give them a big target with a predictable trajectory.
Decent computing power: Yes, yes, we've all heard how the computers on Apollo 11 had less computing power than your cell phone. That doesn't mean that doing everything manually is always a good idea. More powerful computers can automate a lot more of the repetitive work, making space flight easier.
Willingness to take risks: It doesn't matter how many tests you run, at some point there will have to be a first person to strap themselves on top of thousands of pounds of explosives to hurl themselves into space. There will always be risks inherent in doing that. As such, a risk-averse species might never make it to space.
Curiosity: You could have all the resources in the world, but if you never play with them to see what happens, you might never learn that rocket fuel can burn. Also, you would need some measure of curiosity to even want to build a rocket in the first place.
Several Options (best when they're all together)
Resources - When there are at least enough resources to stop chasing food, and start innovating, then technological advancement for an intelligent species can take place more rapidly. Also, you'll need the resources to physically get you off the planet.
War - Part of the reason our space race began with Sputnik and Yuri Gagarin, was due to the Cold War and rigorous technological competition between the world's two superpowers and their allies.
Desire - When there's a delicious planet nearby, and theirs is really rather dull and filling up, your people will start trying to figure out how to go there.
Dreams - Long before our space race we as a species looked to the heavens, dreaming of flying, then dreaming of going to the moon.
Compatibility - If your intelligent race is not "life as we know it," and are able to survive in space and they survive on an asteroid or small planet, it's not long before they can get the technology to get into orbit and beyond. (Okay, this one was a stretch)
The other answers here pretty much sum it up rather well, but I would like to add another characteristic: The everlasting need to have more than what one has.
Societies and individuals both want to have more. You can observe it with businesses, billionaires, and Minecraft video game players that want to have more raw ore. Pick your poison - people seem to be very interested in getting to that next step.
It's the entire basis behind the Kardashev scale of civilisations. Going into space gives you access to all kinds of resources, such as the helium-3 isotope on the moon or an asteroid with 20 trillion dollars worth of platinum, iron, nickel, and cobalt.
And the great thing about technology is that reaching the next step helps you to reach the step after that, and so on. Building computer chips out of silicon, and using computer chips to calculate how to reach the moon, for example. It's all about leveraging current technology.
A cultural and societal mindset centered on undertaking and progressing to that next step will invariably make one's society end up in space. It's basically inevitable.
Probably the simplest marker for a true spacefaring civilization is the ability to move through space and use the resources that exist wherever you go.
This is analogous to a seafaring society in the sense that the seafarers can travel to distant lands and conduct whatever activities they choose. A non seafaring society might have fishing fleets, for example, but the ships come back to shore every night to replenish and prepare for the next day's work. Our own civilization is much like the fishermen in the second example, we can go out to sea for a short time, but have to return to shore eventually.
When our ships can travel to the moon or asteroids and take on local materials to refuel or resupply the life support system, then we will be about 80% of the way to a true spacefaring society. At that point we will be somewhat like the Vikings, capable of crossing the Atlantic for expeditions and plunder, but not really capable of doing too much more on the shores of "Vineland".
The final steps to a true spacefaring civilization will be when there is economic justification to go there, and people can go across the void to settle, trade or build now settlements and industry (much like the second wave of people to reach the New World starting in the late 1400's).
In terms of time, we are pretty close to figuring out the technological tricks needed to become "Space Vikings" and at least visit distant shores for short periods of time. Discovering economic justifications to actually settle space and become a true spacefaring civilization may take much longer; despite decades of research and speculation, there are still no compelling economic reasons to actually go to space.
Imagine a society that knows for sure, the expiration date for the planet on which they live. Let's say for example that scientists have predected that this planet will be destroyed due to a huge natural disaster in about 150 years from now, this will eventually lead them into becoming more interested in space travel and the possibility of finding a new habitable planet out there, in order to ensure the survivor of their kind.
So the fear of extinction is a motive for a society to become spacefaring.