Both of my Uberti '73s in 357/38 run fine with factory length .38 special cartridges.
Here are my suggestions for components.
Brass -- Winchester if you can get it, or find it. W/W chamfers the rim of the case -- which no other manufacturer does -- and that results in a more harmonious relationship between the extractor claw and the cartridge. I believe only Winchester understands that the 38 special might be run in a rifle and that other case manufacturers think it is a revolver round exclusively.
Bullets -- Try some 125 grain Moly Coated Bear Creek bullets. You'll need a LFCD to make this work as they have no crimp groove. Or, Chey Cast makes a great 125 grain bullet with ample lube and a crimp groove for a more conventional approach.
Powder -- Titegroup. Goes bang the same way every time, hot, cold, up, down. Start with the Hodgedon's Cowboy starting load of 3.2 grains. Most of us have never moved on from there -- it works so well.
Primers -- Federal if you can find 'em.
Anywho, that should get you started.