An Altoids Tin is a necessary piece, though your could make the games work without it. I designed everything to interact and be stored inside an Altoids Tin.
For connect 4, you will need to print the game board and 21 pieces in each of two colors. I recommend making the board a different color than your pieces.For convenience I made an stl file with 21 crown pieces included. Just print it in two different colors. I haven't tried painting any of the parts, so if you give that a try let me know how it turns out. I've also included individual pieces of both the crown (used for checkers below) or blank.
For checkers, use the crown pieces (the same as the default 21x stl file for connect four). You'll also want to either make a game board on paper or I'd recommend using the chess board here: https://www.thingiverse.com/thing:2823112. Go ahead an use the chess pieces too if you want as well: https://www.thingiverse.com/thing:2823401
A video demonstration: https://youtu.be/wSXafCYZ4XQ
Monoprice Maker Select v2.1
Using 100% infill works well on the pieces. The pieces can use the extra minuscule weight.
A pass with a file through the slots be be needed or if you have stringy filament, a heat gun/blow dryer may help. I used a metal file to quickly clean up stray strands but did not need a heat gun.