It's a bit of a knack to learn to breastfeed in a sling, and different people find different styles of sling work for them. Personally I find it easier to feed upright in an Asian-style carrier (mei tai or buckle carrier), but, each to her own. So if it doesn't work for you at first, don't give up, as it's possible another style may work better for you - and not everyone manages it. Great if you can, though - as you say, if you have a baby to feed and a toddler to chase, it means you don't have to choose!
With regard to exposure, I find that the sling and baby cover pretty much everything (especially if the baby is in an upright carry, in an Asian-style or a wrap).
Think about clothes you can wear that would offer you some coverage from the top while allowing you to get your norks out in a sling (so anything you have to tug up from the waist is more difficult). I got several Frugi Diva Dresses on eBay, and they're fab as you can get good access without wanton exposure; I also simulate the deep v-neck with liftable bandeau style with deep v-necked jersey dresses worn over separate camisoles.
As for covers - the sorts of covers or coats that you often need to wear over slings in the cold or rain can be fiddly to deal with while adjusting for BF and can make it harder to view your baby when snuggled down into breastfeeding position. I breastfed my DS under a sling raincover with a big floppy hood while chasing DD in the mud, but it meant I had to check him constantly to ensure he was still breathing.
I would think a designated breastfeeding cover would add to these difficulties, and unless it served some other purpose (such as warmth or water protection, I would be hesitant to add another complication.
Whatever you decide, good luck with it! :)