That bike is a great collection of unique high-end racing parts of the day.

Campy Gran Sport rear mech,
Forged spider cottered crank, probably FB or Magistroni, probably marked "Frejus" because that's how they rolled,
Half-step chainring selections, with the two being just a few teeth different in size,
Adjustable-reach stem
Balilla brakes
Gran Sport or Valentino front mech
Ancient bar-ends
Hubs that look like they could be Campy Record high-flange

Those are all valuable parts once cleaned and restored, but they come on a Frejus frame from (my guess here, but based on teh decals) the '50s.

You can fixie it, you can modernize it, you can part it out, but what you have now is about as close to original as any of us are likely to see.

I don't see any frame material stickers, but that doesn't mean it's gaspipe, in this vintage of Italian antiquities. It could be anything from cheap seamless high-carbon steel to a carefully selected mix of Reynolds, Falck, Columbus or whatever else was available in post-WWII Torino.

I hope you proceed carefully and make it work close to the way it was when new. Especially be careful with the crankset.

The only parts I see that might not be high-end of the day are the chainwheels. Simplex aluminum chainwheels were commonly mated to steel forged drive side crankarm/spiders, and yours appear to be steel. If they were replaced when the bike was 10 years old, ok.

The saddle was an abortion when it was new in the late '70s. Probably a Brooks is the closest modern piece that would approximate original equipment. There were Italian leather saddles in those days, such as Aquila.