First , I believe that everyone has the right to choose a suitable teacher for him/her that charges according to his/hers economic possibility. There is no use to start and taking one or two lesson and then stop because we can't afford it anymore. Therefor I will advise you to look for someone that his charges suit your pocket. This way you won't have to stop and change voice teacher in the middle of your voice learning process.
I would suggest you also to try and find someone who can prove his professional abilities as a singer and as a teacher by videos or audio files. I won't just trust his/her word for it. I would also get an idea of what are the results I might obtain from studying with him/her.
I would look for someone who has years of background and teaching experience, and not a fresh one. Usually an experienced teacher can offers you more. No always, as a rule, but often.
I would try to find a teacher that gives you a nice and comfort feeling while study with. Singing can be sometimes like open your heart to a "stranger" and tell about "all your problems. Your teacher should be a person you can communicate with and feel free to be able to give feedback during the process. You should feel relaxed during the lessons for the process to be effective.
Don't obligate yourself for a long period for lessons before you know the teacher and you have decided that this is what you want/need.
You shouldn't feel any strange feelings on your throat at the end of a voice lesson. If you do feel uncomfortable (and you don't have a cold) afterwards that means you may need to change your teacher.
After a while with a good teacher you should feel you can sing much easier, singing higher notes with less effort (than before) and have a clear sound. If none of it happens that means that may indicate on the fact that this method might be not working for you.
Above all: Listen to your body/voice and what it tells you. If you feel that the teacher IS helping you that is great. If not you can stop your lessons , and look for another one. Don't forget , now you have much more knowledge than before to know if things are good for you.