Honestly, all these feelings are completely normal. Not only are you suddenly faced with not having the birth you want, but instead of thinking you'll go into labour 'sometime', they're talking about an actual date.
No wonder you're feeling all shaken up by it!
The reason they won't have mentioned breech birth to you is that most hospitals and consultants don't like to do them. This isn't because they're particularly dangerous (if it's a straightforward breech), but as C-sections have got safer, fewer and fewer consultants and midwives have experience of breech births, so they get a bit nervous. As other posters have said, if you find someone who has experience of breech births and thinks you have a good chance of delivering naturally, then you're in good hands.
Do you remember what sort of breech position they said the baby was in? If your ECV doesn't work (and I'll be crossing my fingers that it does) then make sure you ask them ALL the details - what position is the baby in, where are its feet/legs, is there something physically preventing it from turning over, etc etc. Write it all down if you're feeling wobbly, so you remember it later. Then you have some information to talk to independent midwives about.
Now C-sections: OK, so at 39 weeks, you're very unlikely to have gone into labour before that, first babies are almost always late. If you do go into labour, it's unlikely that it will progress very far before they can take you in for a C-section, as first labours tend to take ages, so it won't be a rush, so please don't fret about that. Unless you're the sort of person who gives birth very quickly, in which case breech or not, you'll have your baby!
I remember a recent post from you about being terrified of the birth anyway, do you think some of your fear of labour/birth is getting all mixed up in this, so it's not the specific procedure that's worrying you, just the whole concept of giving birth? It must suddenly seem very real with all this talk of C-sections and dates and ECVs!
As for the mechanics of a C section, I can tell you how they work if you like, and they're really not anything horrible, but for now you should definitely focus on getting that baby to turn. Relaxation, lots of positive thinking, ring an acupuncturist first thing tomorrow for an appointment, and keep your fingers crossed.
p.s. I know there's been lots of talk on here about breech births and independent midwives - if you decide that's not for you and go for the CS, that's ok too. This is your baby, your birth, and your decision. As long as you're comfortable with your decision, that's all you need to know.