Yes, Unique, Universal Clays, AA #5, etc will do it for you, but, with that selection of calibers, you will really need a minimum of two powders, and three would be better.
1. A fast one for lighter loads in .38 Spl, .45 ACP, and even 9MM.
2. A medium one for .38 Spl, .45 ACP, 9MM, and midrange loads in .44 Mag.
3. A slow one to get full performance from .44 Mag.
AA #2, AA #5, AA #9
Red Dot, Unique, 2400
WST, W-231, W296
Competition or Zip, Silhouette or True Blue, Enforcer
N310 or N320, N340, N110
Clays, Universal Clays, H110
And a number of other good ones not mentioned.
Unique? That's the same as it was 25 years ago
Then you are good to go. Unique is an excellent all around powder.