Cleanest burning?
All powders burn cleanest - most completely with least amount of residue - when used at their top end pressure range. All three powders you list are on the fast to middlin' range of burning. You will find the 'hotter' they are loaded, the cleaner the results. With .38 Special, (standard or +p) part of the problem is the pressure limits on the cartridge are not the upper ranges of a particular powder.
One finds that - for example - Bullseye and Clays are rather clean burning. This is due (in part at least) to those powders burning so quickly even modest charges with either 148 grain or 158 grain bullets run at the pressure limits of the round.
Of the three you list, a glance at the Hornady reloading manual shows 700X as the quickest burning powder in .38 Special. So, it would probably be the cleanest burning, if you run it at the highest pressure loads SAFE IN YOUR FIREARM. This also indicates 700X will give the most abrupt pressure curve of the three.
This is not to say this load will give the highest velocities or best accuracy.
Whereas cleanliness is to be encouraged, it may not always be the sole criteria in any given project.