The German MP38 and the MP40 we developed well after the Spanish Civil War ended.
The two sides used primarily Spanish infantry weapons, and whatever else could be found in Europe.
The primary weapons were:
The various Astra pistols like the Models 1913-1916, the 1921, and the copies of the Mauser "Broom handle", some of these being select fire.
Also the various Star pistols.
The Spanish Model 1893, 1895, 1916 bolt action rifles and carbines.
The Model 1916 was very heavily produced.
Also used were large quantities of Russian, German, French, and Italian firearms.
Russia and Germany used Spain as a proving ground for many weapons, and sent large quantities to either side.