Any hints and tips to get the head immersion thing sorted would be really good for me.
Firstly, the fear of putting your head under water is a natural reflex. It's stronger in some than others but it's nothing to worry about.
Secondly, I taught both my kids to swim by firstly getting them over this fear.
My tip is to buy some decent goggles (Speedo are good) then go to the pool (even your own bath will do).
Hold your nose, take a few deep breaths and put your heard under. Do it in the shallow end so there's no fear.
You should notice that you don't immediately drown.
I did this with my kids long before they actually swam and they really started to enjoy the head under water experience.
Once you realise you can survive under water for 30 seconds it should give you a certain amount of confidence later on.
Next, still in the shallow end. Go to one side, put your head under water, put your hands out in front (fingers together, pointy-style) and push off the side with your legs. Glide for 5-10 seconds and stand up (you know you won't drown in 5 seconds now so it shouldn't be too bad). You ain't swimming yet but just do this until you are happy gliding about .
Once you can glide about and have overcome the underwater anxiety thing you may want to book a lesson because you'll be 80% there. Swimming, especially Breast-Stroke, is gliding with the occasional bit of arm/leg flapping.
Summary, I'd try my best to get comfortable with my head under water as much as possible, in the comfort of my own company, before going for lessons.
PS, a nose-clip helps some people.