Do you have a rough budget in mind or really only just beginning to look/get ideas?
What you want to do is really popular; almost all the from-birth prams on the market offer it these days. Most often you will get a pram which consists of a frame with a handle and wheels, and then into the frame you can slot a seat unit which can face forwards and backwards, and then if you take the seat out, you can put in adapters to take a carrycot or a car seat instead. The car seat adapters are often called "universal" or "multi-brand" which means they take the most popular brands: Maxi Cosi, Cybex, Britax, Besafe, Joie, Nuna and Avionaut. The type of car seat which can go onto these adapters is called an infant carrier, which means it has a carry handle and is designed for use up to roughly a year old.
Some brands like Silver Cross will have a separate adapter which takes their own branded infant carrier seat. Although some pushchair-branded infant carrier seats also fit onto the universal type adapter.
Some of the newer models you'll often find that the seat unit itself can be converted to the carrycot and back to a seat again - this saves space so you don't need to store the carrycot, and saves you buying a separate carrycot - they are expensive as they're only really used for about 3-4 months.
Some more basic models/a more old fashioned type of design is where the seat in the pushchair only faces forward and doesn't come off the frame; the carrycot and/or car seat then usually clicks in on top of this. For those it's usually (though not always) the case that the car seat which goes with it only works with that brand/specific model.
You might want to think about whether you lean more towards needing something bigger and more robust which can handle off-road terrain like woods and beaches and cobblestones, vs something compact and lightweight and easier to store in a smaller car boot or take on public transport. You can get something in between too. But that's usually the starting point.