How do I insulate my unfinished basement with half foundation, half siding?
Waterproofing

Waterproofing the siding should be done from the outside. As in pull the siding off if necessary and replace/repair damage. 
If you are concerned about waterproofing below grade this is something you should look into. It's called dimple board (forgot it's proper, name air gap something or other), but it would require you breaking concrete around the interior perimeter and installing a sump pump and weepers for it to be fully effective

https://www.citywidegroup.com/waterproofing/interior-waterproofing

Insulation

This is what I would call minimalist insulation
https://www.homeconstructionimprovement.com/basement-wall-insulation-detail/

This is similar to the method I would use
https://www.greenbuildingadvisor.com/article/how-to-insulate-a-basement-wall

Your situation is a little different as you have some siding up above. I would continue a plumbline straight-up creating a large void in behind the wall where the siding is. I would then fill that cavity with insulation. I would then apply vapour barrier with acousti seal in the joist cavity's and at the bottom plate. If your plan is to finish the basement make sure to waterproof, if necessary and run all your mechanical and electrical before you insulate. If your plan is just to insulate to make the upstairs more comfortable then you can stop here. 

Side Note the diagrams show a pressure treated bottom plate. We don't do that here in Toronto because it's toxic. We wrap the bottom with a water resistant plastic which is then carried up the stud wall on both sides and becomes part of the vapour barrier.