The 9MM P-Series Sigs can not be converted to .357 Sig or .40 S&W. The frame, locking block, and I believe the extractor and breech face are different.
However I believe you can buy a .40 S&W or .357 Sig model and convert it to run all three calibers. Although at that point I would just recommend a .357 Sig model with the .22 conversion kit.
If you pick up a .40 S&W or .357 Sig model you can swap factory barrels with little or no fitting between these two with no issues whatsoever and the mags are the same.
I have owned a 9MM P226 and currently own the P229R 9MM model and I love these guns.
If you end up with one of the larger calibers I would recommend the .22 conversion kit to save some money for practice down the road.