Oh I am a bit of a bodger and truthfully, my serving skills are nulle, you are as likely to get stuff on your lap, or on the table next to your plate, but not on your plate if I am serving.
I always use eating apples for tarte tatin, and I always melt butter and sugar, for me, preferably brown of some sort, not that bothered which. All of which is au pif, because I was told what to do, but not how much of everything.
Then add the sliced apples and gently cook them until the apples are sort of poached, just cooked in the toffee'ish mixture and then I turn the heat up and slightly brown the apples. At this point, I sometimes add maple syrup, and sometimes IF I fancy a few walnuts too.
This mix, especially with the walnuts and maple syrup is lovely under a crumble.
For a tarte tatin, I sometimes use the baking tin on the hob which I will later top with pastry. But more often than not, I use a frying pan and tip the apples and sauce into the baking tin.