Tyres can be a very important upgrade, the best one can make. I don't know the Vigor specs; I assume it had 406mm wheels. Get a set of light 28mm tyres and matching tubes, tyres with little or no tread. Schwalbe Kojak comes to mind, and my own favourite from experience, Primo Comet, but these are not 28mm btw. I can't think of a 28mm tyre offhand, perhaps a Schwalbe Durano. Pump to say 80psi.
Then if you find yourself limited by the gearing, that you have to pedal too fast, get a bigger chainring. Also, loose any excess weight by stripping off mudguards, racks and non-essential equipment. Keep the chain clean and test the drivetrain drag often by backpedalling by hand; if giving a backwards impulse, the cranks should keep spinning for maybe half a revolution at least.
Fit lightweight barends and cut the handlebar width to be fairly narrow to give a more aero position. Don't let your elbows flare wide, keep them close to your body. Practise to ride with a smooth pedaling action, spinning. Aim to get lightweight clipless pedals and cycling shoes.
That's about it from me.