It's important for newborns to lie completely flat when in a pram/pushchair. That's why most of the lightweight buggies won't do, because the don't recline to a completely flat position. A car seat on a buggy chassis also isn't a good option, for similar reasons. Babies shouldn't be in those for more than 2 hours tops.
That said, I never used a pram with my first. She hated lying in it and I found it bulky and difficult to get around with, so I just ended up carrying her everywhere in a stretchy wrap until she was nearly a year old and went in the buggy.
But there are many good options for travel systems that convert from a pram to a light-ish buggy. For my second I had a Graco Evo, which I LOVE and just now you can get the carrycot that converts it into a pram for as little as £30, do not a huge investment either. I still use it as a buggy for my 3-year-old and will use it with the carrycot for new baby as well.