This would really depend on bonuses, but at this point i think research buildings would be a complete waste

.
It would be more productive to have a manufacturing capitol on your civ capitol, and make as many factories as possible. Then I would place build focus on research. This way you would maximize the number of total points you could extract, while giving yourself the capability to quickly upgrade a planet or pump out ships. I would never have more than zero percent put towards research. It also saves basically wasted research time on a building type.
The second planet I would try to max out the population and income. Maybe put a factory or two on there with a starport for some extra ship support, but I'd probably need the money. This one would get the econ and eventually the political capitol. This planet wouldn't get the array of econ starbases, I wouldn't see a point.
Noting this, I think for once the military starbases might actually be of great use in a galaxy like this, as planet protection is a must.
I would also rush research the terraforming techs and factory building techs.
Trade would be important too, since you're going to need the income. I'd send the freighters from the manufacturing planet because they can build faster, and you can reuse those stacked econ bases as the freighter revenue boosters.
Researching influence boosters would be a waste of time. You can't culturally conquer a planet in this galaxy.
Researching hull sizes above medium is probably a waste too. You can't afford to pump out large or huge ships. Too much galaxy to cover.
Speed is obviously a must.
Galactic resources of all kinds except for influence will be the key to survival. With this strategy you won't need to upgrade research miners, but it's nice to have the resource so no one else gets it.
Weapons wise I'd do some scouting so I knew what defenses to focus on. You're going to want to keep your ships around for as long as possible.
Also, unless you've massively outsoldiered a civilization tech wise, you will have to prep your invasion forces by sitting your transports out in space for a bit and letting populations regrow.
And now that i've done all this thinking... I'm going to have to try this game. This sounds like a completely different approach.