The 'chemistry' when starting the coaching process
You are thinking about hiring a coach, and the offering sounds good. At some point, you probably either pick up the phone or meet up live to discuss details. While you probably have a lot of the technical questions to answer (what, how, how much, where...), please don't forget this is also about the 'chemistry'. This is where both sides decide if it could be fruitful to work together. Like all good decisions, this is partly based on information and partly down to gut feeling.
You are going to share some pretty personal things in the process, and you want your coach to treat this mindfully. You might need help stewarding you through some hairy bit of change where you can't see the end yet, or where you are not sure where to place your foot for the next step, and the one after. You are not sure if you are going to be able to stick with it; you really want to, but you have let things slide before.
Your coach is there to support. They will hold you to account, and they have an arsenal of different ways that they can propose. They will cheer you on if you lose faith or sight of the bigger picture, they will call you out if you keep kidding yourself, and they will help you work through what has happened there. This is all part of the process.
So, you are not looking for a replacement for your Mum or your hairdresser, and a drill sergeant might be a few steps too far. A coach is somewhere in-between. This is not about having super nice conversations where everyone agrees with you, but it should also not be so far out of your comfort zone that you are afraid of the reaction and start self-editing your input to get out of the panic zone. Challenged-and-ok-with-it is a good place to be; it's ok to be a bit nervous or apprehensive.
Ask your coach for examples. You won't be their first client, and they have seen some typical ways change plays out in their field of expertise. Human change can be a bit messy, and it's often not straightforward. Your coach might not be able to tell you what happens in session four a few months from now, but they might give you a sense of how change and coaching processes supporting such change can play out, and what to expect.
This also gives you a sense how comfortable you are asking questions that are a bit weird for you (you are likely going to be doing more of that as the process starts unfolding), and how they work with you in that space (again, this won't be about indulging you endlessly, either). In any case, after getting reasonably real in meeting one you should have a pretty good sense if that is the sort of person you want to work with, and vice versa, and you can then take it from there.
Shop around - don't settle with what won't make sense. Make your choice, and then give it a chance to do its magic.