Necessary parts to build a DIY smartwatch
Any wearable computer project needs these subsystems:


Power - A Li-Ion battery is ideal. This requires a charge controller and regulators to provide your voltage rails. 
Output - You'll find miniature OLED displays that are perfect for a smartwatch. Also consider a vibrating motor for notifications and haptic feedback.
Input - Buttons are easiest to implement. You can also consider an IMU, jog dial, or even a five-way tactile joystick.
Connectivity - Bluetooth Low Energy is ideal for a smartwatch. The HM-10 is a commodity part, but the state of the art does change often. Find one that comes preconfigured with a GATT server to make things easier.
Processing - The state of the art changes too quickly for a recommendation. I've used the Teensy 3.2 for many projects because it's small and Arduino compatible. Find something easy to develop for. If this is your first project, use a development board instead of mounting a processor on a custom PCB - burning a bootloader is complex.
Enclosure - You'll likely need to use a 3D printer or laser cutter. For prototyping, you can simply hot-glue a watchband or Velcro strap to your electronics.


I always recommend prototyping first with off-the-shelf modules, then design a custom PCB once you've tested your project.

If this is a little complex for your project, you could consider a complete off-the-shelf system. TinyDuino sells a complete kit that includes display, power management, processor, and Bluetooth connectivity.

Bear in mind that the computer client will likely be far more complex than the hardware. Slap some hardware together ASAP so you can focus on seamlessly forwarding notifications to the watch and work on your UX.