Duncan Hull had the great idea of Fantasy Science Funding.

In step one, I'm picking the European Research Council (ERC) as founding body.
The ERC is in principle a great idea. Any scientific discipline can apply, from any country of the EU and a panel of referees decides what gets funded and what not. The first thing I would work on is the abysmal funding rate of some of their programs.

In step two (being the chief executive), I'd first invest a modest amount of money into a census of how many candidates I'm likely to get for a specific program and then adjust the funding and the application guidelines of the grant such that I get a realistic funding rate of anywhere between 20 and 70%, depending on what kind of program I want. Obviously, the 20% programs will mean more money for fewer people, the 70% programs means less money but for more people. I want to reward low-budget science as well as high-profile, big science. To reduce the amount of prestige associated with a low success rate program, I'd initiate an award program in which I reward a proportion of the 70% grants with the highest publication/Euro output with a hassle-free, one-click, no questions asked extension of the grant. Now we have a playing field where top-notch, big science has a decent funding level, and those labs with a regular, solid publication record get their grants extended without any bureaucracy involved.
Come to think of it, if at all feasible, I'd set aside a small amount of money for truly low budget science. Small grants for indivduals with almost 100% funding rate. They have to be tiny, only one per person and extension only with publication.

In step three, I get to fire certain areas of science. Here, I would first set up rules to eliminate applied sciences from my funding scheme and set up a separate scheme for that. This separate scheme would be run by politicians and economists who are experts in determining what application is good for our economy and our population at large. They are also directly responsible if their programs don't yield the returns they promised. This separate granting body would also include medical research. Of course, the line is not unambigous, but I'm not too anal about that. If, for instance, your grant invovles a disease, you're in the applied science section, even if you're not working on a treatment. I've never understood why applied research is so well-funded by public sources and why there is such a widespread aceptance of this funding anyway. So applied research is fired and has to go and get funded by a system which is run by the appropriate experts. this includes energy research, nano-tech and robotics, etc.
So now we have a basic science funding agency that funds both big and small science, but still not every single project gets funded. I think there's some value in competition for funds. It just increases your motivation to write a good grant
Me being a candidate for a starting grant, any starting grant programs I'd set up would require that the applicants do not have their own labs, i.e., no graduate students, technicians or anything like this. Not on one of their own grants and not from their host laboratories. They need to be single working units in need of startup funds to start their own group. So I'd fire established researchers from posing as phony junior scientists, regardless of their age. If you have your own lab, you're not getting another one from me! Go and apply for the regular grants.
One big area of neuroscience that I would fire is lesion studies, where you just burn a hole in a vertebrate's brain and see what happens. At least perfuse some drug in there or something but don't just make a hole. I think we've got plents of that sort of data and should by now be at a stage where we can do more refined manipulations. If not, go to invertebrates, find out what some good candidate kinases/receptors/channels/etc. are and then do your refined experiment, but please stop the hole burning business.

In step four I get to hire science. Obviously, I'd mandate some sort of open access publication policy for all my grants. I'd also invest in infrastructure to have a functioning, all-encompassing post-publication paper assessment system working, such that we can factor in this assessment in the paper/Euro equation.
I'd definitely hire what is now called systems biology, but specifically, funding would go to grants studying the most perplexing property of gene networks: robustness/degeneracy. Genomes and gene networks are not fixed and stable as the current systems biology diagrams would like to suggest. They're semi-fluid and flexible. This is one of the most fascinating and exciting areas of biology which is slowly coming to the main stage.
Another area I'd fund is the sort of coherent multi- and inter-disciplinary research program Svante Pääbo and colleagues have set up at the Max-Planck Institute for Evolutionary Anthropology. They sequence all the genomes of all the apes, human and Neanderthal and in parallel perform analogous psychological tests on the extant species. In my opinion, this program is the biological equivalent of the Large Hadron Collider at CERN (which of course is a big HIRE along with space exploration!) and any program like this should get funded. In this vein, paleogenetics in general is cool and deserves funding.
In my own field of neuroscience, I'd invest more in new model systems in general and in invertebrates in particular. The latter investment goes along the same lines as my firing of mammalian lesion studies and combines neuroscience with systems biology: if at all possible get to know the principles in cheap and numerically less complex animals before you muck up a system you haven't even begun to understand. This saves time, money, animals and a whole host of other unnecessary hassle. You'll also learn more about the evolutionary background of the brain function you're studying and once you know the genes, you can interfere very specificly with your brain function of choice.