I was thinking more along the lines of hookers and blow actually.
As for population, we have always had the technology and means to solve overpopulation: starvation and war. In fact, it is said that wars were used as a way to reduce populations -- or a result of that need.
If we wanted to be realistic about solving overpopulation without killing or neglect we'd be investing in new methods of birth control -- not searching the stars for new places to put people. The latter is what a cancer does when there are no "natural forces" to limit growth -- except host death.
Even so, this world can support nearly endless numbers of people so long as the will is there. The sun bombards the earth with 12.2 Trillion watt-hours per sq mile (4.7T/km^2) per year, and there are literally endless mineral and water resources to tap. There is also enough space for everyone on the planet: even 100 Billion people would have 5000m^2 of land area each if spread out over the surface. We'd be building upwards of course, which would house even more people.
The question is: what do we really get out of having more people? Mankind's society has been built on the idea that labor is something important in creating a functioning society. A society without means to work, an outlet for labor, is a dysfunctional society. We see this already with refugees, the unemployed, occupations (Gaza, etc.), even those who choose not to work.
This need to dump labor that makes me think that maybe we will be colonizing places off Earth. We have to give people something to do and build. The alternative scenario is that society becomes more wired together over the internet, and we create and build our worlds there. A giant MMORPG people live out their lives in, accomplishing things. It already happens. The future may be something of both.
Still, as for means, humankind can endlessly expand if allowed.
What would I like to see invested into? For one, a space elevator. It's not so we can go living out there, but rather so we can move things back and forth from space to Earth. This can include weightless labs, disposal of waste, and even energy generation from having an earthed connection to the ionosphere. Though who knows, maybe it'll negatively impact things like weather, communications, etc. Overall, everything would still remain Earth-centric, with space being just another resource. It'd also mean that we could send up bigger and better scopes and probes.
I want to see more advancements in therapeutic cloning and augmentation. I want to experience the world through my senses and abilities, not just read about what "humanity" has accomplished (yeah, great, you were an astronaut, what good does that do for me?). I want good health so that I can see what is here in the world. Sure, I can definitely do more with the time I'm allocated, but imagine the possibilities if you know you have infinite time? We can think in terms of centuries, not decades. I might even bother learning another language, or take a year or two off for traveling, or live a couple decades in some monastery or something.
More immediately, I'd like to see more investment and deployment of better nuclear reactors, such as molten salt nuclear reactors. They'd be quite a bit better than particle-spewing coal or that ecologically disastrous hydro-electric. This should facilitate a move towards more inexpensive personal transport -- not this regressive public transportation trend that comes about from resource costs and/or artificially promoted and funded.