I have a 2004 suburban z71 it will shift from two to four wheel drive without me hitting the button while driving down rd. I've reserched it and it is either the push butto n in side or the actuator what do you think I should by first?

 

A multimeter with a high capture rate or a cheap oscilloscope, a service manual, and maybe a scan tool that can read live data from all modules. If parts swapping is your technique of choice choose the cheapest part or the one that will be easiest to keep clean so you can return it. In this case probably the switch.