Clays Universal and Winchester SuperField will give best results.
Win231 too, is very good for the load profile you're looking for.
For minimun load start with 9mm minimum loads, but expect failure to eject and/or lock slide back until mid-9mm loads are reached.
What you seem to be looking for is something to use in NRA PPC semi-auto matches. Myself and a fellow competitor used the .38 Super with excellent results several years ago, but in 1998 I switched over to S&W P-C guns in 9mm. He still continues to use the .38 Super (He shoots for S/A team)
I had excellent results with 5.0gr of Win231 and 115gr .355" bullets in S/A 1911. (same load I used to use with 9mm too)
Also good is 5.5gr of either WSF or Clays-Universal. Velocity is 9mm-ish at approx. 1,150fps.
These are mid-range loads for .38-Su and are very accurate with reliable function. I would suggest trying Hod. Titegroup if looking for even greater economy, suggest 4.8gr with 115gr JHP's for top accuracy.
Most mid range 9mm loads (powder charges that is, of course) will work in the .38 Super, just remember to seat bullets to ~ 1.220" oal with firm neck tension and light taper crimp.
For 124gr bullet, 4.9 Superfield and 4.7-4.8 Universal worked very well, but cost of bullets offset economy of reduced powder. Could not see any improvement in accuracy over 115gr from 125-5 or 147's.
I used same load in .38 Super with 147 that I use with 9mm, 4.6gr of WinSuperfield. It's above what most manuals list as max for 9mm but is what 2 commercial loaders have told me they use for their NEW ammo.
Velocity is ~990fps. Seat to 1.225" in .38 Super
BlueDot and HS6 and HS7 gave some thrilling high velocity loads, but for everyday general use, the above loads will prove best for .38 Super; unless of course you're loading for IPSC powerfactor. Never played that game so I can't make recommendations.