I prefer someone who does at least some professional playing and better still if they are still 'learning' themself (i.e. commissioning new works, developing new ensembles and projects and so on). That isn't to say all great players are good teachers (they certainly aren't!). If you don't get on with a teacher, change to someone else! I would also prefer someone who has had conservatoire training on saxophone because otherwise there will possibly come a time when a lack of technique will prove a barrier - best get it right at the beginning. Generic woodwind teachers or sax doublers can get you started and certainly help with general musicianship and reading but a good specialist sax teacher is probably better if you can get one. Another good approach is to go on a summer school like the ones Rob Buckland runs at Woldingham and Harrogate. I first ran into him about 10 years ago and he revolutionised my playing and meanwhile put me in touch with a great teacher who has helped both myself and my daughter immensely. These days, there are plenty of graduates coming out from the various music colleges around the UK and they have all been through the mill with the likes of Rob Buckland, Christian Forshaw, Kyle Horch or Gerry McChrystal and they know their stuff. As an adult learner, I found about 1 hour fortnightly worked for me as I could usually get in enough practice over that period. The other important thing is to find other people to play with - anything, a concert band, sax choir, big band etc.