@ Cheapshooter: I think you forgot 9x21MM IMI
I had the same talk with my wife when she was first getting into guns; 9MM seems to be one of the most confusing pistol calibers for new shooters simply because as you pointed out there are at least 4 or 5 common non interchangeable calibers out there that might just be called "9mm"
I don't see where the OP listed exactly what 9MM SIG he has; I can only speak to what I have experience with the P226, P229 and P239. Firstly the SIG "Classic" series of pistols (P226, P229 , P239 etc) is good to go with both standard and +P ammo. I have never used +P+ ammo and have no desire to start.
As for range ammo just about any brand is good to go. Some brands you will find shoot better than others, lots of people like to avoid steel cased ammo and certain brands of ammo because it is corrosive. I use Seller & Beloit, Federal or Winchester mostly.
As far as self defense ammo (hollow points) I have yet to find a brand of ammunition that does not feed well consistently with my 9MM P226 or P229.
With any new gun it is good to try different brands of ammo to rule out any issues with one particular brand of ammo.
I have not had any consistent problem with any brand of ammo. I prefer 147gr and 124 gr +P gold dots, golden sabers and 135gr Hyrda-Shock.
If you are looking for value; you can find 50 round "Law Enforcement" boxes of Gold Dot's for about $30.00/box online.