etane, the original wheels on your bike where Campagnolo Nuovo Tipo 36-hole high flange hubs laced to Fiamme red label tubular alloy rims with double-butted chrome plated steel spokes. They were the same diameter as 700C. You can use those with narrow sew-ups for high performance or laced up clinchers and anything from 23-37mm or width as needed. The frame will handle pretty much any tire. The Universal brakes (probably Sport model center-pulls) will work with either 700C or 27". Original shifters/derrailuers in the late 60's were Campagnolo Record but starting around '71 it was common to see Campagnolo Valentino. That's what was on yours as you can tell from the front derailleur. The original crank is the Nervar. I believe the bottom bracket is 116mm with that crank. The orginal seatpost was plain steel so that might be a later replacement. Pedals are probably Lyotard. The stem is typically a house brand Carnielli although I have seen TTT. Bars are usually unmarked Maes bend, probably also house brand. The 'G' on your head badge is for Graziella. Graziella was another brand manufactured by Carnielli. I have seen that once before. I don't know why that badge was used instead of the Bottecchia eagle.

The wheels are the big problem on your bike now. My bike, set up for centuries weighs just under 25-lbs and has a lively, springy ride. In "race" trim with tubulars it weighs 22-lbs and feels as light and quick as my relatively modern Bianchi.

Here's my setup built with Nuovo Tipo hubs and Rigida AL1622 touring rims and 700x28mm tires. First picture is with Nuovo Record rear derailleur, second is with Campagnolo Rally long cage and 14-34 freewheel for assending Pikes Peak: