1) How the nails look when done. On my own hands, I love getting unique, custom designs/hand painted designs etc, and so finding a tech that does this would (if I didnt do my own) be my priority.
2) As Trinity said, longevity. It would be boring to have to come back for repairs frequently. Accidents can happen, but if it's a regular occurence with lifting/breakage, then I would consider my options...
3) I don't like feeling rushed, either as a client or as a tech. A rushed environment would not be ideal for me.
4) I'm not a big chatter, and whenever I am getting a service I prefer to just kind of escape into myself and be quiet and relax. I am probably in the minority about this though. But when I'm getting any kind of service, I prefer a professional who can read those cues and not keep forcing conversation on me.
5) Price vs quality. Many techs charge an arm and a leg for just mediocre quality nails. I am OK with paying for a service, but the quality should reflect the price, and vice versa (I wouldn't go and expect perfect instagram nails from a new trainee who charges student prices, for example, but trust me. SOME people do! lol).