How to decide between a vocal coach or a singing teacher
It completely depends on your experience and training.
If you have little/no experience or singing training, then a singing teacher might be best. They will teach you how to warm-up your voice correctly, and can choose music to guide your learning.
There are a number of different teaching and singing styles- you may wish to learn through the "Rockschool" system or the more classical Trinity Guildhall or ABRSM graded system. You may wish to learn "Bel Canto" (Lit. "Good Voice", the classical Italian technique often called the basis of singing) or Speech Level Singing, or you may just know you want to sing jazz, or pop, or rock, or classically! There are many teachers out there, male and female, teaching in many ways. I would suggest you have a trial session before committing yourself to regular lessons so as to be sure you feel a rapport with your teacher, and enjoy their teaching style.
A vocal coach is better for someone who is a confident and trained singer, who is looking for someone to work on their repertoire with, in general or for a gig or an audition, or for someone looking to have a regular "vocal workout" session to keep their voice strong and flexible.
In both instances, who you chose is personal choice. Some may say that, if you are learning to sing, you should learn from someone of the same gender; I have not found this to have a great difference positively or negatively, apart from when working in a specifically high vocal range for which my female teacher was able to show me what I was doing wrong.
Neither are cheap, but your voice is not something you can replace if it "breaks"! You can expect to spend anything from £25 for half an hour. Only you can know if a teacher or coach is right for you, so always have a trial session, and do not feel embarrassed to look or sound silly in your lesson, as sometimes exercises can feel silly!