In my experience, there are three type of instructors (there may be others, but if so I haven't met them yet):
The first type is reactive, (s)he just tries to "quick fix" whatever your problem is. You can easily book a single lesson here and get a view pointers to what you're doing wrong. This usually is okay if you can't figure out why something that used to work suddenly stops being effective. Typical lines you'll hear from him/her: "keep your head down", "your shoulders are not aligned correctly" and "try standing up a bit (less)".
The second type teaches a "standard" swing type. You'll soon get bored here and chances are you will not really improve (but he/she may shave of two or three shots from your average score). Things this type of instructor change may feel strange and don't be surprised if you'll get hurt in the process. Typical lines: "let's try some stack and tilt", "let's start with the basics: grip".
Than there is the third type that really analyzes your game (he may even accompany you during a round) and adjusts it to match your possibilities. From this type, you may expect some quick improvements, followed by more substantial improvements in the longer run. Typical lines: "first, we'll play a round together" and "let's make a plan of attack".
I have worked with all three types. Currently working with "the analyzer" and progress is slowly picking up speed!
So, it's all up to you
. What do you expect, how much time (and money) do you want to invest?
In the end, you must click with the instructor. If it doesn't, look elsewhere.