Ok, I searched the forum, but didn't see anything that simply or directly answered what I'm looking for.

I have the stock brushed aluminium 16inch rims with P225/55R16 (BF Goodrich Traction T\A H/V...)

I found a set of rims that I like (which is hard enough) that fit on the Cat, 17inch rims...

Question: when increasing the rims size (diameter)... is there a rule or way of selecting the proper size of rubber?

16 inch = P225/55
17 inch = PZZZ/XX

etc...

ntnt

That I knew... I was just curious since so other posters where talking about some 18, 19 even 22s... I'd hate to have the rims dictate the type of tire I use... example if the 235/45-17 were only available as All-Season 'Granny' touring tires.... then the rims loose their shine

(just an example).

is there a rule or way of selecting the proper size of rubber?
etc...

yes. there are many website that have wheel diameter calculators.

enter in your tire specs...it shows you the diameter. some even have a nice comparison feature, enter in 2 sets of tire specs and it does a comparison with a number of metrics.