Not aware of any 'rule'. I always installed same thickness base/door trim. To me, one or the other being thicker looks wrong.

Going modern :) thank you! Should I go with the ticker one 3/4 or do 1/2?

thicker one

I think it's personal preference. The 3/4" is more standard (and 3/4" smooth lumber is more commonly available at box stores), but 1/2" might be easier to wiggle around imperfections on your walls. If you're painting the poplar (rather than staining or clearcoating), it doesn't matter as much if you have gaps - caulk and paint make a carpenter what he ain't.

The 1/2" sounds more minimalist to me.

Good luck!

And 1/2 is cheaper :) thank you!

will paint the poplar

I think 1/2" would look more modern. I have been using 3/4" trim with traditional 1/2" baseboards and it is looking a little clunky. But I'm fine with it - looks more craftsman to me. I also put an extruded edge around the window casing to make it look more finished. So the window frame comes out from the wall about 1-1/8" total. (This actually takes away from the "clunkiness".)

Definitely make sure the door casings are flush with or thicker than the baseboards, since the baseboards will butt up against the door casings.