Jason,
Welcome to the World of Tigers! This is a good place to start on your journey and you should find lots of information available.
The easiest way to tell what series is your Tiger is to look at the VIN plate. It should be on the right side of the cowl, above the firewall.
B9470001 - B9473762 Mark 1
B38200001 - B382002706 Mark 1A
B382100001 - B382100633 Mark II
There are a few letters after the number which relate to whether the car was a British export and which side is the steering wheel on.
Since you car is registered as a '67. it is unlikely that it is a Mark 1. In case the VIN plate is missing and you can't find the title, there are some differences that you can tell by looking at the car. If it is a Mark 1, the rear corners of the hood are rounded and not squared. The same is true of the rear corners of the doors and of the trunk. Some of the early Mark 1A's had these rounded corners as Sunbeam was switching over to the newer style. The Mark II's look quite a bit different. They never had the strips running down the side of the car, broken at the door seams and at the "Tiger" script in front of each door. Instead, they had stripes made of black and white tape running just above the rocker panels on both sides. The grill for the Mk II looks like an egg crate, unlike the center motif with a single vertical bar on either side of it as used in the Mk 1 and Mk 1A. The Mk IIs also had molding around each of the wheel well lips.
A lot of these items would have been removed from the car when your dad stripped it, but hopefully you have all of the parts.
Good luck with your car!
David