It really depends on what you're trying to do and the size of your galaxy. If your trying to achieve tech superiority, the tech capital is key in building up a planet capable of doing so. There have been many that have built up some pretty amazing tech planets. Search for "tech" and you may find some of these posts. These planets are pretty much exclusively PQ32's built with tech capital and omega research center and nothing else but research buildings. Then to top it all off this planet should be surrounded by 16 economic starbases fully populated to give a 24% bonus (that's 24% per SB, 384% total) to research. With this kind of treatment you can achieve research rates of 16,000 to as high as 20,000 RP's per turn. This generally requires you also have a good handful of research resource's to mine.

On the other hand if your galaxy is small and tech is not really the focus of your strategy then plop it down wherever it seems to do the most good. Although from your description it's probably best to put it on the highest PQ planet you have and convert everything on that planet to research even over building factories (and starport and anything else) with research buildings. I assume that you know that you can get production out of research buildings by using focus.

Also the planets population has no bearing on the research (or production) it generates. Population only relates to income and morale not to research or production. A pop of 1M will produce the same as 20B.