They are not high-performance or a super reliable workhorses, but they were not meant to be. For motors, I chose to use 28BYJ-48 uni-polar stepper motors. They are common and inexpensive. However, in the CoreXY configuration, they barely have the torque required. Generic linear rails with more traditional cartesian kinematics are a bit pricier, but more effective.
For pen lifting, I used a common 9g micro servo. It works fine for the purpose.
On the electronics side, I used an Arduino Nano and Darlington array uni-polar stepper driver boards (commonly shipped with the 28BYJ-48 stepper motors). You can find wiring diagrams for a very similar setup using an Arduino Uno online. The Nano is running a modified version of GRBL, based on this fork. I recommend using a standard Arduino Uno, as the Nano's usable flash space is a bit too small for GRBL with CoreXY kinematics enabled, requiring the removal of some unused GRBL functions. The Nano is powered over USB by a computer, and the steppers and servo require additional 5V power, provided through another USB cable.
I use my Patherator software to generate G-Code for it. Inkscape with a G-Code plugin would work well too, and is easier to install if you don't want to mess around running Python scripts.
To run the plotter on the go, I send G-Code to it with my PocketCHIP running a simple serial sending script, and a common cellphone powerbank provides power for the motors.