I am not quite sure what you mean by "staining".  Tween and triton are detergents not stains.  Do you mean, which to use to permeabilize the membrane before using a specific membrane protein stain? In that case, it depends on your cell type and amount of permeabilization. Tween and triton come in a variety of forms, but basically tween is a less stringent nonionic detergent than triton. For mammalian cells, typically I recommend to start with 0.1%-1% tween and if that doesn't work move on to 0.1%-1% triton. Keep in mind that the more stringent the detergent, the more membrane will be disassociated. 

Sorry, I meant for immunostaining. Tween/triton-X would be used for permeabilization in this regard. I have seen people also argue that no permeabilization is needed for surface proteins. Just trying to gauge some different opinions.

If you want to stain plasma membrane proteins for which the epitope is located on the extracellular side, you should not permeabilize.

  To my knowledge saponin is also a good choice to minimize disruption of membranes during immunofluorescence procedure.

Dr. Campbell-Valois is correct.  If your going after a surface, extracellular, protein then there is no need to permeabilize. If the protein is intracellular or transmembrane then you need to permeabilize. Saponin, tween and triton are all good options use 0.1%-1%. Methanol or ethanol are also options if all else fails. However all proteins and cells are different, start with saponin or tween-20, then move on to the triton, then as a last resort ethanol, then methanol. This is also the order of stringency, so the saponin/tween will do the least damage to the proteins/lipids, while methanol does the most damage.