What resources would be most valuable to enhancing space travel, establishing new colonies, be cause for invasion, etc?
It's hard to say without knowing what technology the colonising societies are using. Prior to the 1930s, Uranium's primary use was as a yellow pigment. Nobody could have guessed how valuable it would become!
It's also important to remember that there's almost no material substance that could be gained from invading another star system that couldn't be acquired more easily from asteroids, moons, or other celestial bodies. If you can travel between the stars, you can meet your material needs quite easily.
So for the moment, let's put aside the notion of conventional resources; they're just not rare enough to drive conflict or colonisation. There are two other things that might.
We're already starting to see something of this in the modern world. The limiting factor in a lot of situations isn't the availability of raw materials, but access to the information and knowledge needed to take advantage of those materials. A situation where wars are fought over the control of major data archives or universities could be imagined.
This is the one thing we've discovered that seems to be genuinely rare - indeed, unique to Earth, so far. The complex chemicals produced by living things, indeed the complex process of life itself, seems to be rare, at least in our solar system, and so are environments that can naturally support life. A war could be fought over access to life-bearing planets, or perhaps planets where a particular form of life can grow (echoes here of Dune and the Spice that can only be found on Arrakis).
If you want both information and complex chemistry, and a base of people ready to use that knowledge, then a large population with a developed economy would be a useful thing to have. Wars might be fought over the right to exploit a given population, with whole worlds changing hands. An interesting wrinkle would be that all parties would want to keep the fighting away from the planets, to avoid damage to the prize.
All of Them
Spaceflight occurs at the end of a large, interconnected web of technological development.
You need chemistry, refrigeration, pumps, metallurgy, electronics, computers, precision manufacturing, structural engineering, medicine - with math underneath all of those.
You also need 'soft' technologies like project management.
For any kind of long-distance space travel, like colonizing other bodies, you need biology and even more chemistry.
The resources needed for spaceflight include ~30 elements on the periodic table, all sorts of compounds built up from those elements, and the knowledge and skills to turn those compounds into useful (and often very complicated) objects.
There's no one thread you can pull out of that tapestry and call 'the most important' or 'the biggest target for invasion'.