What is the best was to splice electrical wire to power two components? (Arcade power supply and LCD

[gnuuser]

Some great advice,here,but the solder is not necessary,if the crimping is suitable. Indeed,depending on the conductor type,and machine operating conditions,it could be detrimental.

I've got the loud,vibrating type of arcade machine,in mind

when using din rails in a machine with a lot of vibration, always torque the terminal screws down to the proper torque rating, and add a drop of enamel or thread lock to the top of the screw, use a sharpie to mark the position on the screw! (this can help in diagnosing possible issues with loose screws)
as others have stated din rail terminals are widely diverse and suitable for many applications.
but they do need to be in an enclosure.