If you have a harbor freight nearby, keep an eye out for a coupon for a free multimeter with purchase. They are cheap, not very good, but you can see if you have voltages and continuity. Very basic, and if you mess up and read voltage while resistance is selected and you burn it up, you're not out anything.
If you really want accuracy, nothing can beat a Fluke. However, for EM machines, I don't worry much about accuracy - I just need to know if a switch is open or closed, and if I have coil and lamp voltages. Since this is brand new to you, get the cheap meter to start with and work your way to a more expensive model as you get a better understanding of what you're trying to read.
Just my two cents