I've had two children far enough apart they both had different prams. With my first I had the Bébéconfort (now Maxi Cosi) Loola Up and this was absolutely brilliant - the only fault I could find with it was that it was heavy when folded up, and a bit wider than it felt so sometimes you'd clip doorways, shop shelves etc with the wheel but never had an issue fitting it in buses, car boots etc. I loved the way the seat went both ways, loved the reversible seat cover, loved that you could wash the seat cover in the machine and it dried in a day! It laid flat without a carrycot which was important to me - used the main seat right from newborn.
I prioritised some of the same things again for DC2 - parent facing option, proper lie flat seat (many these days are what they call an "ergonomic seat" which just tilts backwards leaving them in a sitting position, which is no good from newborn), highish seat, but I went for bigger wheels. Looked at and almost bought Joie Chrome DLX / Cybex Balios S (note, not the new 2 in 1 version but the original Balios S) but found a really good deal on a second hand Mutsy Evo and went for that.
Verdict - it's OK, but the harness is absolutely rubbish, really hard to adjust, much too big, I've got it the shortest it can go and DS2 is only just fitting in it as 2, and it's still loose on him. OTOH the seat is shallow so he was constantly sliding down in it and being suspended on the crotch strap, and the backrest is really short - his head is poking out the top and he's only 2. I wouldn't buy it again. I think I'd go for another Maxi Cosi! I liked the Stella and Adorra although there are probably newer ones now.
I did get an umbrella stroller for both of my boys but it was only ever an extra stroller, for days where we wanted to fit loads of things in the car or when I knew I'd be taking buses which are often busy, that kind of thing. I used the proper from birth pram right up until the end of not using one at all.
I would recommend you look at the Maxi Cosi Stella, Adorra, and Joie Chrome (whichever version they are on now).
I'd defo get an infant car seat, Maxi Cosi Cabriofix or Joie Gemm, so it can go on the buggy (both use Maxi Cosi adapters) unless it's only one grandparent's car and you can leave the car seat in there. Otherwise you're stuffed if you take a bus one way and get a lift the other :)