Do you recommend playing one path first over the other? Like would it contribute to the story flow- or simply pick whichever cast one prefers?
It depends on a few factors.
If you would rather have a slow start and save all the most interesting events for later, start with the P3 story, since the events in it are more down-to-earth and have a generally slower pace. The story feels generally less densely packed with events, so it feels like a warm-up phase. Also, you get Yu being a fatherly badass to his team.
The P4 story is far more densely packed with development for both, the P3 and P4 characters, there are more events and more conflicts between the characters, and you also get Makoto Yuuki, the most deadpan, quiet person with the weirdest kind of humor of all time, and he's really worth being seen.
What which story you pick *shouldn't* depend on is whether you like P3 better or P4, because, in all honesty, both teams are equally relevant in both stories. It's really just different in which events you see happening between them during the dungeon explorations.