I used mine a lot. I'm not particularly shy, and can feed discreetly, but it meant that I was comfortable feeding wherever and whenever (such as tube where seats face eachother). I don't use it much now (8 months) as I think I'm past caring, but for those early months when baby fed a lot it was invaluable.
I used my big floaty cardigans or a Muslin. I only know one person who had one, but it's a personal choice. Try bf out at a playgroup or similar where it will be common first until you build your confidence
Back when I was breastfeeding I went out with DD for lunch with my parents. There were several mums breastfeeding. I only noticed this because I was looking for it and was doing it too. The only breastfeeding mums who were extremely noticeable were those wearing the big aprons. I think it's far more unnoticeable to feed without one, or with just a scarf to hide any bits of tummy on show.
I am a very 'discreet' feeder. Like that woman in Claridges who made the news. But I have a Bebe au lait. They have a loop at the top so you can easier see baby and breast. I can't get on with giant muslin at all. I only use the cover when going out with male friends or relatives. It saves them the embarrassment on not knowing where to look.
zennudist I could also say scarf and muslin are unnecessary. I carry neither and I don't normally use a cover. What's wrong with just babys head as cover? That's what I nornally use.
But the OP wants to consider one and Id say they are better than a scarf. What's the use of a Muslin really? The difference between a no cover is that you can put baby in front of you with the cover over baby and still see clearly your breasts and babies head. They have a metal loop at the top for viewing.
I was given a second hand bebe au lait one. Used it a few times but agree a scarf is actually easier and looks better. I only really needed it while faffing with nipple shields and breast pads. While baby is feeding there is nothing to see.
I never bothered with one, but used a muslin in the early days while I was still building my confidence. I wore a vest top under my top, and pulled my top up and the vest down, so there was no exposed tummy. If I wanted extra cover I tucked the corner of a muslin into my bra strap on the side DD was feeding, so I could drape it around her so that there wasn't any side-boob on show. A scarf probably does the same job while looking much more stylish!
I prefer to wear a nursing vest under a long sleeve t-shirt. Bra and vest come down under boob, t-shirt comes up. No tummy on show, and no boob once baby latched. A casual checked shirt on top, open, assists with obscuring any side view. This is my breast feeding uniform and is far more discreet than any cover I tried.