Just swinging by quickly to talk to Brookeberry about slings and prams...
If you can change the BB carrier, I would, as you will probably struggle to carry the baby in it for very long as they're not very good for your back.
If you possibly can, go to a local sling library and try some out there before buying. I started off by renting ones then ended up buying a few of my faves. Just before DD was born, I had a sling consultant visit me at home and show me how to tie a stretchy sling (it's a bit of a knack as you need to get the faric fairly tight but smooth on your body). I then rented a Hana sling which is a bamboo knit and very breathable so comfier in warmer weather than some of the cotton ones (Moby is the most popular stretchy one but I found it too thick to use comfortably).
Then when DD was 4/5 months old, we rented a Manduca buckle carrier which can be worn on front, side or on the back for older children. DD is 3 in a few weeks and still fits in it, so we have had our money's worth (we bought a second hand one).
We also have a Scootababy hip/side carrier which is great for popping out quickly as it's a single fastening.
Final word on slings - be careful when buying the v sought-after brands such as Ergo as fakes are very common, even when buying new off Amazon.
Re pushchairs - we got a Baby Jogger City Mini GT and it's been great - can be folded flat with one hand and doesn't take up too much space in the car. We bought adaptors to attach the car seat to it, although didn't bother with a carrycot (although may get one to put on it for this baby). Loads of space for shopping and adjustable handle height for taller people. It also has a hood which reaches over to cover entire passenger plus two little windows in hood so that you can check on your sleeping offspring
We also have an old McLaren for trips abroad plus a Bob Ironman for running