Welp, I normally start with a factory or three, just to ensure that the rest of the improvements don't take forever. That strategy sounds about right, though for the really really big planets (I got a PQ-26 the other day) I like to balance it out. This one planet was both my tech AND my manufacturing capital. Probably not the best way to do it, but meh.
Economic planets want lots of people. Ergo, lots of space, and higher PQ planets... I guess.
Manufacturing planets want to be able to make a given thing as fast as possible. Medium planets stocked fully with your best factory districts work fine for this.
Research doesn't care about the size of the planet. Where an economical planet of like 5 pq can't rack up the combination of population and economy that it needs, and a manufacturing planet of that size wouldn't be able to make anything worthwhile in any useful time, a RESEARCH planet simply puts all the output in the race-wide research stock, be it 1 rp or 100. So you can safely put research stuff on tiny planets.
Now, I tend to set each planet to do all sorts of things, like I said. I'll have a lab or two even on a manufacturing planet. I'll make a starport on almost every planet, as well as a couple morale districts and maybe a farm+economy. After that, all factories or all labs unless I'm making an economy planet.
Did I mention that I'm kinda new at this?

I THINK that most of what I said is still solid, though.
Also. I like having constructors. I'll set all my planets that have starports to make my latest model constructor and send them all to a single rallypoint near my borders, then start expanding my influence. This worked wonders for my Evil-aligned game as the Yor in a friggin' huge galaxy... free starbase upgrades, I believe? And as well, my standing military was so powerful it was able to just sit around looking important while I took over half the galaxy with influencer starbases alone. Nobody even peeped about it except the Iconians... who were summarily executed for their impertinence.
Funny thing is, my standing military was very small by most standards. I just had enough production in enough planets that to go from making my uberconstructers (40 movement!) to a fleet of superdreadnoughts would take far less time than actually doing serious damage to my empire. Strategic depth FTW.