OK, it's not hard, just drawn out.
It would be enormously easier if you had a wiring diagram.
But - here's how to approach such a fix.
First, we have to figure out a few things. This will make it easier.
One - I'm guessing you have 240VAC, yes?
Two - The connection for the Pre-Heat light is to those two brass points in the back of that pretty little white bakelight piece. One side will go to the neutral line, one side will go to the connection on the new thermostat which will either say 'P' or pilot-light or indicator light.
You can test it (I assume you know the safety procedures) first with standard 120v current. If it no longer lights or flickers badly, you can replace the little neon lamp easily, it's a standard part.
Three - how are the broil and bake element wired up? Sometimes they are completely separate from each other, other times they share a wire between them. Rarely, there are other set-ups.
I'm going to assume the most common here - when the broil is on, the bake is off. When the bake is on, the broil is off. They may have four separate wires or only three. If it's three, take a picture and post it so we can tell you how to procede. It's not hard, either way.
So - a clear wiring diagram came with the generic thermostat. There will be (not necessarily with these names, could be numbers with the key to them in the diagram):
L<sub>1 </sub>and L<sub>2 </sub>These are where the power goes into the thermostat. It should come up straight from the connector for the plug to the range.
P or Pilot or Indicator or Lamp - this is turned on when power is going to the oven. It may turn off during the bake cycle to indicate that the P-H level has been reached, then turn back on a gain when it turns the heat back on again. It probably stays lit the whole time the broil element is turned on.
You will have a wire coming up separately from neutral for the other connection on the pretty white bakelight piece. It may come up straight from the connector to the range's plug or it may come (more likely) from a group of neutral wires running to other lights or outlets. It's no big deal where it comes from.
There will be either three or four connectors left. If there are four, two of them will go to the broil element and the other two to the bake element. If there are three, then one will go to one terminal on each element and the other two will be be hooked up, one each, to the remaining contact on each element.
There are variations, but, basically, this is how it works. If you give us a link to the generic thermostat control, we can probably find the wiring diagram and that, together with good pictures of the elements and the back of the range controls, etc., will be enough to help you piece this together so it works safely and reliably for decades more.
Gosh - how pretty!