While I think upping your %research (at the race creation level) is a pretty obvious way there are some things you can do no matter what race/bonus you are using.
I spend a period of agony every game trying to figure out my core research world. Its tough because the earlier you get it set up the better off you are but theres nothing more frustrating than finding a class 28 with rings and research bonus tiles the turn after your tech capital is completed elsewhere.
What I try to do each game is find a high quality planet and maximise my research output there through a combination of tech capital, research coordination, omega research and economic starbases (by installing the production/research modules). If you set it up right it can end up producing more research per turn than every other research world you have put together.
The key here is stacking a lot of %research. Secondary to that is trying to fit as many other planets as possible under the starbase bonus and making them research (or production) worlds. But always focus on the number 1 planet as the techcapital and omega bonus dwarfs the potential of any other planet.
You can fit 4 starbases per sector so another thing you may want to consider is how close a planet is to the edge of a sector as it can allow you to overlap it with starbases from other sectors as well. It all depends on how heavily you want to throw money at this - just the 4 starbases works fine.
You are not always going to find a high quality planet thats suitable but thankfully you have some options in creating one - it just takes a little bit longer. When colonising low class planets keep an eye out on how many yellow tiles are available and calculate its future class. Often even a lowly class 1 can end up your research capital on the basis that it has 5-6 yellow tiles.
Another option is setting up shop on an extreme world but its the slowest option. It can be very rewarding in the long run if that world is of a very high class but it is much easier to set up a non extreme tech capital - even a low class one. You don't suffer a period of production penalty while waiting for the colony techs and work can begin before you even think about looking at researching extreme colonisation.
The sooner you get this world running the better as otherwise you are likely to start to fall behind the AI. Also the starbases do not really need to be built for quite some time but its handy to start building the constructors early. The percentage bonus they give does not really start to shine until you have a planet covered in the upper end research structures and they start generating hundreds and hundreds of bonus RP.
Its worth noting that you pay less for research generated through bonus production. Also having a very strong economy so you can afford to fund a lot of research is very important. You may find you lag behind in research because you cant afford to fund it and therefore hesitate building more research or adjust the slider down.