I'd go for Arduino compatible for the first iteration, because Arduino schematics are publically available, so you can use them as a reference, they don't need many extra components and are somewhat forgiving if the voltage regulation isn't perfect. More complex microcontrollers have embedded PLLs that require a very stable supply voltage, usually fed separately, that is a complication you can probably do without for now.
In general, you'd get the datasheets for the components you want to use, which list the requirements for the component to work, and usually also has reference design fragments (because the engineers that designed the component already had a general idea how it would be used).
Typically, you need
- the microcontroller itself
- capacitors to stabilize the power supply
- a regulator to provide the appropriate voltage(s)
- a crystal as a time source
- a connector for programming
- whatever peripherals you want
Most microcontrollers already have a bootloader in ROM to support programming them in-circuit, e.g. via USB DFU or through a serial connection.
For voltage regulation, a linear regulator is easiest to use, but generates quite a bit of heat. Switching regulators are more complex to build and get right, so I'd do that as a separate project (I did that once and optimized from there). If your microcontroller requires multiple voltages, go with an integrated solution that ensures sensible power-up and -down behaviour.
The crystal is a bit tricky to get right, but for me it worked on the first attempt, so it's certainly doable -- keep the connections short and use SMD components.
Other than that, it's fairly simple, because most of the complexity is hidden inside the ICs already.