And they are using new site, Biontech in Marburg (a reporposed existing facility if memory serves well), Sanofi will be ready in summer to produce the Biontech vaccine as well. These things take time, rushing them is never a good idea.
All of them. Or at least all of the different kinds of factories (mRNA, vector, live vaccine) for the most promising candidates. If there is a shortage of something, force production, apply imminent domain, force cooperation. War against Corona should be handled like a war, not like a toilet paper shortage.
Done right, one could even get away with not reserving the second shot from the first deliveries. Another parallel between toilet paper and vaccines is the sudden demand spikes, read additional orders from the EU in January, that resulted in reduced short term availablity.
Ideally you spread the doses over a few weeks or months so that you can stop the vaccinations should any issues arise. I'm not saying the current distribution is fine, it's far too slow. But not even Israel has vaccinated everyone in a single day, nor would that be a god idea.
This is btw also the way Google play distributes updates. Instead of every user getting the update right away, they first give it to a small group, then that group increases gradually in numbers.
Maybe your specific country handled things around covid great, but not the place I come from, not its neighbors, not the place I live in currently, and not its current neighbors (covered some 15 european states by this in east & west/south).
Money spent on vaccine infrastructure would be absolutely nothing, especially when pooled by few/many states together, compared to havoc covid is wreaking on economies and still will in incoming months, no way to avoid it. Plus the small benefit of actually saving many lives should also hold some, not only political capital.