Original std tyre size on an RA28 is 165 R 14. They have an overall diameter of about 522mmm. To keep your gearing and speedo close to original you should try to get near the same diameter, so on a 16 inch wheel you want a 205/55 16 or a 205 /50 16 or 225/50 16. Above 225mm you run the risk of your tyres rubbing / fouling the guards or suspension. I sometimes run 225 50 15's on my RA23 and have no rubbing problems.
Tyres alone won't give good handling by themselves, they should be considered as part of your total suspension upgrade. Given that, lower profile is better and some tyres do handle/grip/perform better than others.
Case in point, Goodyear Eagle GA's are a poor tyre, Yoko A539's are much better, by xomparison.
In 1977 Toyota never considered low profile tyres on its cars so its suspension design would only reflect the best tyres available on the day.