We did both NHS ans nct classes with our first pg.
The NHS classes were focused on when to go into the hospital with contractions, they went through pain relief options, but were very g&a and anti epidural, nct was the same really. There was a feeding antenatal ass too, very much focused on bf, rather than bottle feeding.
Wrt the birthing plan, I just followed the questions on the form that the mw fills in. Like how you want to birth ie, on all fours, pain relief, if you want baby cleaned before handed over, if you want dp to cut cord, if you want skin to skin, cord blood donation, when you want cord cut, that sort of thing.
I did ask for a water birth with dc2, but did put on the form that if the pool was not available, then it wasn't a problem. Although I was 8cm when I arrived, so it was all very quick.
It's a shame they don't cover ff much in these classes and seem to put pressure on about bf. But, I bf both mine, and then ff, so would have been nice to get some sort of info on it, more the how to make a bottle up safely. What they don't tell you about bf, is that you can encounter problems feeding. That isn't covered, which is a shame.
I'd try and get another class if you and your dp really are unsure of it all. I did find the hospital visit useful though.