There are lots of options for this. You can go with traditional headers like those, if you need higher density than normal 2.54mm headers, you can go to the half size, 1.27mm which is still pretty common. You can also look into mezannine connectors, which are what are typical for very low profile, high speed board to board interconnects.
Maybe have a search around digikey or your preferred distributor to see what is available and then look around to find the best price.