Good thing not to be afraid of labour - you'll be fine and the baby will come out one way or another as you say. Have ideas about how you would like it to go, but keep an open mind until you are actually there and doing it for real, as to what you want.
If it's painful, you can take drugs - no prizes for suffering!
When my DD came out, I gave a last push to get her body out, she slipped out into mw's towel which she had in her hands, mw gave her body a little rub while passing her to me and she was skin to skin on my chest for a while with the towel over the top of her. She went pink very quickly and cried very quickly, and within a few mins was getting her chompers on my boobs!
I actually don't remember the cord being clamped or cut; think it happened very quickly - I was so busy looking at DD's little hands and little pink lips, and at DH sobbing, (bless!).
I guess they must have sewed me up downstairs (had episiotomy) while I was holding DD in one arm and munching toast, chatting to the Registrar sitting between doing the stitching (had epidural so cdn't feel a thing). Don't remember anything about the third stage either though did get a look at my placenta. I think once baby's in your arms (and you have TOAST!!) the rest of it just passes by in a whirl without you noticing.
After a while DH held DD and then the mw took her off for weighing (same room) and a clean up, and DH put her first nappy on and first sleepsuit (it was so sweet - he was so so gentle and nervous with her, it took him about 20 mins to put one bodysuit and hat on!)