About wheels, I'd keep them if they're worth keeping. In other words, are they true, or true-able? Are they 700c (622 ISO size)? Do the rims have hook bead? My spouse has a Bianchi with straight bead wheels, so I know they're out there. I have a rule which is to only build wheels out of good rims. Life is short.

And of course you can still find tires for 27 inch wheels (630 ISO), but the selection isn't as good any more.

I've done conversions, but typically on bikes where the wheels were already unsalvageable, so I didn't have to sweat over that choice.