Condition of the m/w should tell you if it is worth putting money into it. But that said about $150 in parts is cheaper than a new one, so if it were me, I'd fix it. You will need to remove the oven from the wall, by the 2 or 3 screws holding it to the cabinet, remove the outer shell of the m/w, then I can point you in the right direction from there. I will give you the easy way to disassemble the inside

First remove the oven from the wall, and set on the floor.
Tip it on it's back, and remove the bottom. Next, remove the grille above the door, 2 screws.
Tip the m/w back up, and remove all screws from around the outer case.
Now stand M/W up meaning the hinge side of the door is now on the floor.
There is a metal plate as you are lookin straight down at it. should be 4 screws, right, back left, and one behind the control panel.
disconnect the wires from the small black cap and tco that are attached to the metal plate you just unscrewed and set aside.
Next remove the 4 screws holding the transformer in place. Don't remove the wires from the transformer. just let the transformer sit there and move it to the back right corner.
Now remove the wire plug on the magnetron and the 2 wires on the mag tco.
You need a 5/16 deep socket to remove the 4 screws holding the mag in place, and remove the mag. You will need to twist the mag a bit to get it away from the fan assy.
Now put it all back together, just make sure when you hook up new mag and the wires that the wires do not interfere with the fan blade.

If I forgot something let me know

Do I need to short anything?

Just ordered AP2631638 (GE). I guess all I need comes in this kit. What's the capacitor's part number?

Just wanted to know what I was shorting :-). You're the best!