I am using a nice clean burning round. I prefer Jacketed bullets for handgun ammo. I have used wadcutters in the past but now I don't need perfect holes to measure. My load probably is not even close to the cheapest good load you can make. It works for me.
Bullet - Montana Gold 158 grain hollow point.
Powder - WST (Winchester Super Target) 4.0 grains.
Primer - Winchester Small Pistol
Any major manufacture's small pistol primer will probably work just as well.
WST is a faster burning powder than W231 is and gives a nice soft feel when shooting. It also does burn clean. WST measures very well in most powder measures.
If you think you need more speed you can use a slower burning powder like WSF or AA5. You will get more recoil and speed with them. I use the 158 grain jacketed bullet for .357 mag. It seemed reasonable to use the same bullet for .38 special. I like this load and is all I'm using now for specials.