In reply to Frank4short:
This formula in MS Excel produces a result for overall tyre diameter.
=sectionwidth*aspectratio/50+(wheeldiameter*25.4)
Wheel rims should be about 80% of the sectionwidth figure: maybe +/-5%. Tyres in mm and wheel rims in inches!
=sectionwidth*0.8/25.4
Example
195/65 R 15 91V
sectionwidth = 195
aspectratio = 65
wheeldiameter = 15
result for nominal tyre diameter = 635mm
result for wheel rim (80%) = 6.14 inches (nearest real rim is 6 inches)
It doesn't matter that the calculated diameter is not the same as the actual rolling diameter. It is a good enough figure to use for comparison with other tyre sizes.
For instance, 165 R 15 has the old default 80 aspect ratio. The calculated diameter is 645mm which is within 2% and therefore close enough.
The calculated wheel rim is 5.2 inches and the nearest real rim is 5 inches.
You then have to determine what is available and what can be afforded.
These days, narrower is always good. In winter, it's very good, and it also makes it easier to fit chains. However, the starting point is the size you have fitted as standard and this may be the cheapest option. Although as a general rule big tyres are more costly than little tyres there are some market influences that distort that so look carefully at the costs for different sizes.
Email me if you want a copy of a spread sheet already set up for some tyre ranges.