I look for balanced players in general. Four adjectives sum up what I look for in a player: skill (technical attributes), smartness (mental), athleticism (physical) and passion (hidden mental).
Skill depends from position to position, but I look for decent techinique in general and then emphasize the more specific attributes for the position/role you're looking for.
Smartness relates to mental attributes in general: anticipation, composure on the ball, concentration, decision-making, positioning/off-the-ball and the most important attributes: teamwork, workrate and determination.
I look for relatively fast players in every position and with decent stamina. Strength and aerial ability are also valuable, specially for defensive players. Natural fitness is the most important physical attribute though. And I like tall players.
Hidden attributes are the most important. I recently realized that determination isn't the attribute what makes a player develop the most: ambition and professionalism are. That's what I look for the most. The other ones, as previously said, are also important.
Injury-proneness needs to be the lowest possible (10 or lower) and high consistency and versatility are very important, since I like to have small squads (23 players or less).