I'll first put my disclaimer out there and say I'm not an electrician.
First, pictures are worth a thousand safety tips. Can you add some pictures of the existing panel(s)? Adding a run has it's challenges. The cable size, type, conduit type are all determined by length of run, amps, and location; might be 1 or 2 others I missed.
As far as adding a sub panel, there are some very strict code and guidelines that must be followed. Namely, the previously mentioned. If this is something you're thinking of doing on your own, be sure you know what you're doing. I had been in the trades for nearly 20 years, and I've played around with electricity plenty. When it came time to adding my sub panel for my shed, I decided there's too much to account for and know to do it myself.
I believe you would be able to do what you're looking to do with relative ease. You can tell your service by the breaker size of your main panel. If the main throw is rated at 200A, it's safe to say you have a 200A service.
As I recall, if your run is interior, you would need to run metal conduit and need no less than a 4 gauge stranded run. If it's exterior, you would need to run schedule 40 or 80 non-metallic conduit. Either way, the cabling needs to be stranded.
I would suggest calling a local electrician to verify gauge for service size and run. It's also good to note, there are specific height requirement, panel types, and grounding requirements that must be considered.