My thoughts on navigation:
How about a button that toggles between 1x, 2x, 4x which affects the scaling factor of all zoom and pan buttons?
I think a combination of this, a 'fit to full data' button and a rectangle zoom tool would be most intuitive to me.
I think the zoom in and out should default to affecting both axes equally and have zooming axes indepedently as a special case.
If you implement a zoom rectangle, there should be a way of locking its width-height ratio to be the same as the current display, perhaps by holding CTRL down.
I think it's important to always have an easy way of zooming out to show the full plot, so if you implement your saved view idea and don't want to add a 'fit to full data' button, I think having a 'fit to full data' checkpoint automatically added is important. It might be even be worth looking into cacheing the full view to speed its rendering. That way, you could quickly navigate by zooming to full and then using a rectangle zoom to your area of interest.