I don't know your specific application, but probably for fixing the gel, i.e. preventing the diffusion of protein bands and the subsequent lost in resolution, sensitivity, etc.
Acetic acid and methanol solution are generally used for protein fixing in gel. This solution denatures the hydorgen bond in protein and exoposes hydorphobic part. Also thus this exposed large size of protein will get trapped into gel thus avoids permiability of proteins from gel.
It serves for two purposes. first it will fix the proteins thus preventing the blotting and spreading. Secondly when the gel is fixed in the solution it can be analysed in second day. These are the two primary objectives of doing so. Some people also use water instead of acetic acid and methanol solution to preserve the gel and analyse it later but doing so have been reported to cause fungal growth in the gel (sometime).
The stacking of gel into acetic acid solution will hamper the visualization so i suggest not to.
Since the difference between the gel-fixing solution and the gel-staining is only the coomassie stain, both solutions would "fix" the proteins equally well. The reason for using the gel-fixing solution first is to remove the SDS bound to the protein first so it will not compete with the coomassie stain.