If you want to try then do just that
I've been breastfeeding DS2, out and about for the last 8 months and barely anyone noticed.
I've never had any negative looks or comments, people in Costa have brought me drinks when I was pinned down cluster feeding.
The only "reaction" I've had while breastfeeding was when we were out for a meal with a lot of friends for DPs birthday. I was chatting away and helped DS latch (quite discreetly, no one could see any part of my breast) and it was only when I paused mid-conversation that our friend noticed I was feeding DS, turned his head away and said "oh OH, shit, sorry!"
We're the first of our friends to have children, most don't even have nieces or nephews, he had no idea how to act and thought he was being rude by not giving me privacy. It was really quite comical, we had a good laugh about it and since then he's been completely un-phased any time I've fed DS2 around him.
I thought it was going to be really difficult to breastfeed discreetly, as I have huge boobs that are always in the way. flowing tops with a nursing vest underneath work really well!
Normal vest tops will be completely fine as you're small chested.
We bought bottles just in case we needed them. We're only just starting to try him with them, as I'll be going back to my course soon.
Good luck, enjoy 