So there are a lot of things that I consider before I purchase a game, but here are my top 5. Also, I won't rank them because they are fluid based on the game, sometimes one may be more important than another.
Mechancis - Does the game include mechanics that aren't present in a game I already own? Does it have a new take on a mechanic I love? Do I even have in interest in most of the mechanincs?
Theme - Is it a theme I'm really attracted to (a few examples are, Star Wars, the Wild West, Cyberpunk, etc)? Is it a theme I don't care about at all (I don't really care for Real Estate or Environmental themes for instance.
Player Count - As I've noted before, I have almost no use for 2P only games. I actually prefer 5+ Player games as I tend to have 4, 5, or 6 people at my game nights. Also, I have a few 4P games so those already come out when I have 4 or less so I try to focus on "the more the merrier".
Player Interaction - Is it basically multiplayer solitaire? No way am I getting it. I don't mind if it's lighter on the player interaction, but typically the more the better. It's why I like #Scythe (but wish there was more combat) and one of the reasons #Root is my favorite game.
Components - Are the components high quality with art I love, or are they lacking. Something like #The Expanse is totally out for me even though I love the IP because I hate hate hate screen shots.
Honorable Mentions - Price, Replayability (though I don't usually ever have an issue with this), Solo Mode
What about you, what's most important when you are thinking about buying a new game?