The basic rule of thumb when deciding on a file size for a given saw-tooth size is to select a file where the width of the flat sides are just slightly twice the length of the back of the tooth (the longeer portion of the two sides of a tooth). This means that you use fresh file-teeth as each pair of sides wear down and keep the shape of the teeth and adjoining gullets as small as possible, while avoiding unused parts of the file and maximising the cutting area.
Personally, for a 14 to 16 TPI saw I would select a 4 inch xx slim first because the radius is smaller than the 4 inch x slim….. sadly they are hard to find - at least I can’t find any, so for that size of saw select the 4 inch x slim. For bigger saw-teeth, select a file with wider sides, keeping to the same rule.....
As an explanation, saw files were sometime (and confusingly) called 6-side files when they are, in fact, triangular. They have three straight sides connected by three slightly curved edges. It is this curve that cuts the rounded gullet or point of the saw edge. Most of the stress in use is at this point and it’s usually the first bit to wear out when the sides are still cutting well.
My preference in the UK is for Bahco….. it’s what I’ve always used. I take the point that the gullet radius may be generous and it is this part that determines the shape as the saw teeth get bigger.
However..... saw-files are getting expensive! You won't get a lot of change out of ten-quid for a good file.