OK so, I'm pretty new to GIMP, so I'm still working out basics.
Problem: On some layers, when I try to erase, instead of revealing the little checkerboard or layer beneath it, it just erases to white.
I just want to be able to erase one layer to reveal the one beneath it.

right click on the layer in the layer dialog. go down to where it says add alpha channel (transparent) , click that. you should then be able to erase with out showing the white.