To me the Petite star Zia pushchair ticks all of the boxes. It is by far my favourite of all other lightweight buggys I have tried, which include Quinny, Chicco, Obaby. I got mine when my son was around 8 months old.
Firstly it is clearly a very compact pushchair, when we originally got it it was a holiday buy, I knew I would use it all of the time, we were planning a family holiday and needed something small in order to fit suitcases and travel cot in the car too. The zia fits in the footwell of my 307 under my sons car seat meaning it is in nobodys way.
The fold is very easy, There is a safety bar at the top of the buggy that you clip down, then its two grips on on the handles and it folds into itself, with a clip to hold the two sections together. Under the footrest of the buggy is a handle for use when folded. To unfold it is a 2 second job again, just unhook the clip the buggy folds out and pull up the safety bar and you are ready to go.
My son is very comfortable in his Zia, and always happy in there. it has a simple lay flat recline for when he does sleep, which is adjusted via a strap so it can be at any level, rather then set levels.
The suspension on the pram is brilliant, you can bounce the pram which gives a nice soothing motion for baby. It has standard 5 point harness with adjustable length straps.
There is a small shopping basket which is great for a few bits.

The only small flaws I would point out is that, it comes complete with a raincover but it can be arkward to put on but with a good tug it goes on nicely, and it folds up nice and small to fit in the basket.
One other thing is the handle dont adjust and can be low, im 5'6 and I havent had a problem with it, I just noticed it was lower then my old pushchair, and now I find it quite nice that my arms are out straight when pushing.

Overall it is a fab pushchair, lightweight and tiny.