First, it's the genre. If it's story heavy (like detective case, visual novel type, and especially horror games) or puzzle, I'd avoid it. There is little to no chance I'd play a game like that. It at least should have a battle. And no, not the default frontline battle system, neither passive sideview battler where the battle sprites just sit there for a sake of sideview and do nothing but as an animation punching bag.
Visual comes in second, it's not required, but it also not a cover that I would judge. Cool, a game using custom asset on everything, basically top tier graphics, parallax mapping, custom menu. But if it has no interesting game (and battle) system, I don't think I'd give a chance (or even I give it, it likely won't last long). I don't mind a game using RTP, because it's to be expected when you play a game made by RM anyway. I'm used to it. As long as the dev isn't ******ed like putting a wrong tile
Story comes last, If the screenshot and game feature itself successfully bait me, then I'm gonna learn the story by playing the game. Most of time, I didn't read the game story through the game topic. It's better for me to learn it in game. How well they present their game to a complete stranger.
Edit : Also because of my internet, I'd have to limit the game size. A game might looks cool, but if it's big, I might think twice. An oversized game (200mb+) that mostly just RTP, I don't think I'd give a try, why not make an RTP free instead because I already have installed RTP in my own system.