Just like manufacturing, research takes longer when your production slider is over to the left. The proportion of your spending as determined by the military, social and research sliders also haa an effect. The initial colony tile provides some research at each of your worlds but if there isn't much funding the research takes a while. When you add dedicated research facilities on a planet, there's more research that can be funded through the sliders.
Economic starbases can also give a bonus to your research and manufacturing, and you only pay half as many credits to finance the extra as you would for the base research points.
As for early colonial rushes, it can be good to establish quite a few colonies early on because in the beginning you don't have tile-effective ways to improve morale; so having places to ferry your homeworld citizens to is a nice thing. Long before you ever get troop transports, you can use colony ships to move citizens between your planets. I wouldn't rush to grab every old world though, as every colony costs maintenance right off the bat. The ones with asteroids close by make for good choices because once your space miner has set up mining outposts, those colonies that are seeing the benefits of mining operations have more industry points, and that's great for cranking out the next wave of colony ships. More to the point, you don't pay maintenance on great big rocks like you do for factories.

When you need to spend some of your hard-won tax money on research, those worlds that aren't near to asteroids and aren't likely to be churning out lots of ships make good colonisation targets. Most importantly, planet quality determines how many tiles are initially useable. So far I've never seen any bonus tiles (improvements to morale, research, manufacturing etc) on tiles that need improvement to become useable, so planet quality should be a rough guide to which worlds you want to acquire first.
That said, some low-quality worlds actually end up with a pretty decent PQ once they've received some tender loving terraforming, so whether you rush for them depends on just how long-term your plans are.
On the whole, a rush for colonies can be worth it later on because of the tiles you will have available to generate income and do research and manufacturing, but only if you can hold onto them and only if you can eventually run your economy with the production slider over to the right.