A practical way to connect is use 2.54"connector header bar (female, 40 pins), then cut* in appropriated size and solder the wires in this bar pins - can use heath shrink to reinforce/protect the solders and looks nice - and plug the bar in Teensy connectors. Result "PnP". BU0836 include this connectors.
Dont make solder direct in Teensy pins, the temperature and current transients of solder iron can kill then.
I am not fan of breadboard (other for experimentation), this result in a mess of wires that can induce electrical noise.
Since Teensy is tiny what can help is make a support PCB with more pins. But for your project is not really needed.
For cables is recommend the "pig tail" type (multi copper wires with Teflon like insulation) used in telephony. Dont know the technical name - never see one.