I try to have a team character, and base attributes for each position. Meaning, as a baseline I want players to be fast, and determined. There can be the RARE RARE exception, but they would have to really be something in all other areas. Then for each position I will have a 'list'.
Defenders who can jump and head the ball better than any one in the league preferably, on top of positioning themselves correctly, and being able to tackle. Concentration, marking, team work, work rate, anticipation, all help as well.
Full backs need good stamina, and should be able to match up well against most wingers (i.e. they need to be fast, but since this is a baseline requirement already...) If they are defensive or offensive thats fine, I just won't settle for mediocre.
I have a 'thing' for 2-footed players, and one position where I have found it esp. helpful is in central midfield, as it really helps tick things along. Very difficult to close down a central mid who can use both feet, has good first touch, is a creative passer, and makes good decisions. Just makes the opposition look silly, mostly. I like CMs to be good at just about everything, but if I have to sacrifice I concede jumping, and then heading, bravery, aggression, natural fitness... But they should be able to anticipate, position themselves, be good off-the-ball, have good stamina, you get the point. I demand A LOT from CMs. Its a crucial area.
Wingers should be able to anticipate, it helps a lot with getting the crosses in the right areas.
I think when I first started playing FM (some 10+ years ago when it was still CM) I looked for fast flair players. Now I look for determined players who make good decisions. The difference is immense! I ended up with some really one-dimensional players with my old criteria, now it seems I am able to see future stars a mile away. Also, don't forget their personality, and how it fits into your team.