Well, by the looks of it those are 48 spoke wheels, and the tyres are not that narrow either. So the bike may be old, but pretty fit for purpose. I think you should still fit the widest possible tyres. They are way more comfortable, and that will also protect the bike from vibration. Also, you will have fewer punctures, and on real roads they are faster.
Have a close look at your gearing, and see what you can change. Steel chainwheels don't cost much, and 48-38 instead of 52-42 would make a difference. Similarly you may need a new cassette anyway, and if you do, get a wide ratio one, perhaps even an mtb one (a cheap mtb rear derailleur does not cost an arm and a leg). For the brakes, maybe change the cables, and perhaps the brake pads: on my old road bike proper Koolstap Salmon pads made quite a difference.
Have a close look at your gearing, and see what you can change. Steel chainwheels don't cost much, and 48-38 instead of 52-42 would make a difference. Similarly you may need a new cassette anyway, and if you do, get a wide ratio one, perhaps even an mtb one (a cheap mtb rear derailleur does not cost an arm and a leg). For the brakes, maybe change the cables, and perhaps the brake pads: on my old road bike proper Koolstap Salmon pads made quite a difference.