Safety first. That means tires, tubes, brake pads and cables.
Forget about Jagwire. Its a waste of money on that bike.
Then do the shifter cables and any other work to the shifting system.
The chain looks rusty. Probably needs to be replaced.
Rotate the bars down so that the drops are parallel to the ground, set the stem height to fit you and rewrap the bars with fresh tape. Any tape will do - you don't need $40 Lizard Skins.
And then cut down that Pampas Grass. It is a nasty, invasive species and an eyesore.
-Tim-