What kind of therapist do I need to see?

I am looking into seeing a therapist for my relationship with my son, but I'm really confused as researching online. There are at least three kinds that could be helpful: LCSW, LMFT, and psychologist. I just don't know which kind I need to start with. Please advise!

Very briefly about my situation, I don't think I have a good relationship with my son who is about to going to college this fall. We live in the same house, and that's probably about it. We rarely communicate, and when we do, the communication is very superficial. I get it and admit that I'm a bad parent who is inpatient and didn't spend a lot of time with him when he grew up.

My son is close to my wife and would tell her things about schools and life etc. I think my wife sometimes spoils him too much and also think my son needs to see a therapist because he recently told us that he has been anxious because of the stressful college application, how much he dislike his entire high school time and feeling leftout. I told my wife that he needs to see a therapist, but she and my son told me that I'm the one who should seek help. So here I am.

I feel the whole situation is sad. I do care about my son, but it seems that our conversation often escalates to yelling competition whenever I try to give him some advices. I don't know how to improve this relationship and want to give it a shot before we both check out.

I want to start with some individual sessions to make sure I'm in a good mental stage, and then perhaps convince my son to see a therapist for a few sessions to make sure he is mentally strong before parting to college.

Thank you in advance for your input.