Im struggling with strollers too but yes get one that the carseat can go on because if the baby falls asleep in the car you can just lift it out without disturbing the baby i just came across this which is the cheapest one i have found that comes with everything but i cant find any reviews https://www.babyearth.com/contours-by-kolcraft-contours-bliss-4-in-1-stroller-system.html
I thought I was all set on one of those "travel systems" where the car seat can be just transfered onto the stroller, but then read that it's not recommended to leave a small baby (most articles said under 3 months) in a car seat too much, as it's not good for their developing bodies; lungs and spines especially. So it seems better to just use the car seat in the car, and then have a stroller that lies flat (like a bassinet on wheels) for going for walks, etc.
I doubt I'll be going out much at all when the baby is tiny, so not too worried about it anyway, but if I do happen across a good deal on one of those flat infant strollers I will definitely snap it up. They don't seem to be super popular here in the US though, from what I've seen.
I've been struggling for WEEKS to find a good travel system. I want something highly rated, definitely no more than $200, easy to use, has good buyer reviews, and I'd like it to be somewhat cute.
I found this: https://www.walmart.com/ip/Baby-Trend-Jogger-Baby-Travel-System-Millennium/14005459#Product+Reviews
Not the prettiest looking thing but it seems to have everything I want, even if it is a tad bit over my price range. I wanted to stay around $130-$150, but no big deal.