It's a Samsung TV, several years old. I'm not 100% sure if its 1080 or 720 (I'm guessing if it's 1080, it's probably 1080i rather than p, since I think 1080p is relatively new).
Here is the cable I bought. It says in the answered questions that it works with the Surface 3:
Amazon.com: Cable Matters 101019-6 Gold Plated Mini DisplayPort Thunderbolt Compatible to HDTV Cable, 6 Feet - Black: Electronics
I just tracked down how to change the resolution on the Surface, so I'm trying to find info on what the TV supports.
One thing that seemed odd to me is that when I connect the cable the Surface recognizes the TV, but when I have it identify the monitors "1|2" flashes on the Surface like it's both displays.