Hey there, dire_chinchilla!
If you have an original OEM/retail Windows OS with the product key, you don't need to buy a new one. The operating system communicates with the motherboard, so as long as you don't change that you'd be good to go using your old installation.
If the OS was pre-installed on your computer - you just need to install the same version of Windows and once you go online, it will activate automatically.
If you have the original Windows OS installation media - once you get the SSD, simply plug the USB/DVD and install using the same product key.
I don't think you'll face any issues whatsoever, but if you do, make sure to contact MS support to activate your Windows over the phone.
Hope I helped!
Good luck!
SuperSoph_WD