Unless I've played previous iterations of a series, then I check reviews and gameplay videos. I try to find neutral viewpoints or one overly positive and one focused on bashing said game. I'll check the pricepoint which means I won't usually buy any games that won't last more than a week if it's over 30$ or so. I tend to avoid any subscription games despite playing WoW for way too many years. Difficulty is never a factor because I enjoy both easy and challenging games alike.
Depending on the genre my general criteria would include: (usually in this priority)
1. Gameplay
2. Pricing
3. Controls
4. Story
5. Longevity (replay value and/or consistent content addons)
6. Graphics
I would put Fun at the top, but that mainly comprises my own tastes and a combination of my list. I used to like balanced games, but barring chess there are few that even attempt this. (and actually do remotely well) Anyways, depending on the genre I would completely change some things around. For MMO's Longevity (regular content additions) and controls are very much close at the top. If I'm playing for the story, then I usually like some nicer graphical elements to it. Due to many games being overpriced, I play most games when they are outdated and select only a handful when they are current.
Sometimes an interesting cover will get my attention and I have bought games before due to hype or "it looks good", usually regretting it. I'm sure I'm missing out on many great games, but there is only either so much time or money one can invest. Console games are often avoided due to price and constantly needing to purchase a new console.
D3 was my last "hype" purchase and while the game has become much better it was a huge letdown. It's better to analyze the pros and cons of a game if you are tight on money and/or time like me. It's fine to expect a decent game, but the rampant hype that surrounds many upcoming games inevitably kills some games and the experience when you expect so much.
Conclusion: I look for a good value that provides entertainment value for my interests.
Gameplay(determines fun factor) > All