I can't really advise you on the use of Miliput having never been able to master the stuff myself, so the following will be reference to those individual putties listed. But, first thing I thing would be to keep the finger prints from getting into the putty to begin with, make up some sort of handle and don't touch the actual work. A simple wood dowel with a pin in the end works nicely for smaller pieces, for larger ones it might be well to use a block of wood or even larger diameter dowel. Just remember that this thing is meant to be a handle so should fit comfortably in your hand.
Smoothing Magic-Sculp can be accomplished with water, saliva (bad practice I think), lip balm (this was Quang's idea and works well), and the various other things already mentioned. Water would be my personal preference, it doesn't cost anything to get from the tap and works wonderfully well so long as you keep your smoothing brush only damp with it and not wet. You won't want to flood your work with water it is a bother, sometimes damages the putty if still very soft, and makes it difficult to see what you are smoothing. All this applies as well to MS blended with GS (green stuff-kneaditite).
For A+B putty, water when soft, Acetone in a pinch, especially if the putty has begun to cure before you've had time to smooth. Just remember not to do more than dampen your brush with it, this stuff, like water, is a solvent and will dissolve your putty and make a mess if you use too much. In fact all the things, excepting perhaps the lip balm, I've heard recommended for smoothing are solvents in a way.
For myself I hardly ever file or sand, and almost never on a finished surface-But when I do I finish off with nothing finer than 320 grit sand paper. For a final glossy slick finish, which I don't think necessary if the original is to be painted, I simply spray-lightly, very lightly-with Testors Gloss Coat. This stuff, if properly used, puts on a very thin film of paint, thin enough that it has no discernable effect on the details of even the smallest pieces. The only reason I can think to seek a shiny finished surface is for reproduction and that only because molds used for resin casting seem to cast better with a slick, shiny surface than not. In all cases I don't think I'd be at all concerned about the putty being discolored or dirty in appearance. After all, the finished piece is either going to be used to make a mold or be itself painted so who cares, or will even know?
Were it me I would switch putties and use something like Magic-Sculp or Aves, or as a last resort A+B putty. However, as there are those that have great success with Miliput if you are one of these then I would stick with it even knowing that MS and Aves are a better bargain overall and will keep longer, thus making them more economical in the long term.
Finally, try to use a good quality brush-and keep it clean-for smoothing. Brush lightly in the direction of, say a fold, and across the thing only to remove any light brush marks you may have left with the main brushing. You might also do a little light shaping with a dampened brush when the putty is very soft, especially useful for truing up a seam or the edge of clothing.
Good luck, and I hope this hasn't been preachy and helps a little. If you have any additional questions please ask some one of us is likely to have an opinion or technique they favor.
Ray