“Given that we have limited resources, what would you say is more important, that it looks good or it's technically accurate?"
As the product manager, your job is ultimately to make it both. The trick is to break the problem down into discrete product "moves" such that each move is both beautiful and functional.
The process is not to figure out what resources you have and then work backwards to something you can ship. Your job is to figure out what you believe the user needs and figure out how to marshal your resources to get you there.
Usually, that requires you to create a shared purpose and mission for your team, a reasonable roadmap of discrete releases/moves and the discipline and focus to keep everyone's eye on the prize.