We were given a M&P travel system, which is heavy, but was perfectly manageable when DS was small. Now he's bigger, he's in a cheapo umbrella fold pram, because they're lightweight and they work fine.
So focus on what you need for a small baby. A little extra weight will be a nuisance to carry upstairs, but by the time your baby get big enough for it to really be a problem, you'll probably be switching prams anyway. Don't worry about having one from birth to four, because buggies are very affordable.
With that in mind, i would say to go for something secondhand, as you know that you won't get any reuse from a subsequent child, and that they'll only be in it six months to a year or so. (Though that time will drag if you get a pram you hate, so it's worth paying a little extra for the ease of lifestyle!)
Can't say I muck like the threewheelers, because there's not much room for storage, and having worked in retail, I can tell you from sitting on a till all day watching mums that they will tip at the checkout if you load up the handles a little. Depending on what your apartement is like, making multiple trips to carry a pram up will be something you probably get used to - you won't get a pram and all the weekly shopping up in one go anyway. So don't rule out the bulkier ones that come in two parts, because that last part of your jounrney is a lot shorter than pushing around a pram that is stiff, or too low or high, or doesn't have anywhere to put a changing bag. We have a very narrow door, and getting the pram out was a pig, but when we actually were out it was a dream, despite being a bit heavy.
It's all about compromise in the end, but you can at least cut down on cost by getting one secondhand (and see if family members have old prams lurking, because you'd be surprised...), or looking on sites like freecycle. Just because it's not brand new doesn't mean it's no good. (And it's simple enough trying out models in mothercare then wandering off looking thoughtful if you want to be sure before you bid on eBay or elsewhere!)