I want to buy a 3in1 stroller, max 600€, with a good car seat, for all terrain types (we live in a city but we will be on macadam roads, hilly paths, etc. very often). Can you give me some suggestions, please?
I see what you're searching for but it's rather hard. If by a good car yeat you mean a quality, ADAC tested car seat, that alone usually costs about 150€, so the stroller system itself will be actually a cheaper one. For it to be multifunctional on most terrains, it usually takes a higher price for the stroller to be quality and long lasting.
In any case, for the city, I would absolutely go for a relatively lightweight and compact one, in this price range one with larger-than-usual wheels, and that would be a Joie Versatrax or the Joie Finiti. These are, of course, not the most luxurious ones but very good for the price, with larger tires filled with foam so similar to inflatable wheels with no risk of a puncture, and... well, the price-performance ratio is simply good. YOu usually find these in a 2in1 combination set, so with that, ģet a Joie Gemm car seat which is one of the cheapest ones that are actually safe, tested with a good result as well. Such a 3in1 pram/system should be in your price range.
Another way would be to go for a non-reversible seat stroller system, meaning a world-facing pushchair with a carrycot and a car seat. From Joie Mytrax to a pre-loved Baby Jogger City Mini plus a bassinet and car seat adapters + Joie Gemm, you should be fine.
Lastly, I'll mention the hybrid/convertible Casualplay LOOPi Allroad which is a very cool option with a good-in-the-price-range Casualplay car seat - IF you can get your hands on it (if it's available where you are).