There was no 'standard' sidearm for SS troops - they used the same pistols as the rest of the German armed forces. Photos can be found of SS trroops using everything from P.08s and P.38s to Radom, Browning HP and even 'Broomhandle' Mausers, plus officers' 7.65mm pistols such as Mauser HSc, Walther PPK etc.
Early in the war the SS was less politically powerful and the Wehrmacht got first dibs on equipment distribution. This led to the Waffen SS using a lot of captured or otherwise non-standard equipment. So, "standard issue" and "SS" doesn't necessarily compute. Also, WWII was just coming out of the era when officers were expected to purchase their own sidearms.
A pistol that was quite popular with high-ranking SS and Heer officers, as well as fighting troops in the field was the .32 ACP caliber Sauer 38H. It's virtually unknown in the US/UK when compared to the Walther-designed P.38 and PPK. It is also seldom appreciated that the Wehrmacht routinely issued captured weapons whenever practical, including the Colt M1911A1 as the P.660a.
