How to choose a stroller if having to tackle stairs daily?
TL;DR: Go for something very lightweight and carry home first your baby, then the folded stroller, or get a robust, more expensive (= high-quality) stroller that can survive being pulled up the stairs rearwards. Think of a quick-fold, lightweight, forward-facing stroller with a carrycot and car seat adapters accessories as an alternative.
As with any stroller, pushchair, or pram, there is A LOT to consider. An everyday need to carry your stroller is a lot to ask and big stress on the chassis comparable with very difficult terrain use. In any case, search for quality, or be prepared for your stroller to reflect the strain after some time.
I want to suggest two ways of approaching this situation. It would be best if you thought about which sounds closer to your needs and pick depending on that. It's always going to be a compromise. Think of the basic need of getting your stroller up the staircase as the priority. Don't try to ask for much else, or you might end up with a stroller not being suitable for what matters the most.
The first approach
The first solution that you might be thinking of - and rightly - would be to get something lightweight(-ish). Mainly in the situation where you plan to carry your child first and a (folded) stroller/chassis after that, a lightweight model is the way to go. Here, you can even afford to go for a more budget-friendly model that's mainly going to serve you the first year, year-and-a-half. I, myself, would buy something under 10 kg, ideally. Of course, counting on that, it's not going to be an all-terrain ride. An Uppababy Cruz or a Baby Design Smooth comes to mind as examples. After that period, get yourself a mid-size, lightweight, forward-facing, quick-fold pushchair - and life will become peachy again. A way to go, in such cases, could also be getting such a stroller right from the beginning and add a carrycot and car seat adapters to that (think of Oyster Zero or Baby Jogger City Mini GT2, for example).
The second approach
The second approach would encompass a heavier, full-size model of high-quality and excellent driveability - something in the likes of a Britax Go Big2. Such a model can be pulled up each stair rearwards, on rear wheels. This won't, however, work for those living on the 8th floor ;-) A Bugaboo Fox2 or a Cybex Priam with the possibility of a two-wheel ride could also be a way of doing it. Being pulled up in that configuration could be of help, mainly to the taller parents.