Ive done a lot of ipad digitizer replacements. Your best bet is to avoid touching or getting it dirty to begin with.....BUT ALAS. It does happen.
Personally i use a VERY clean microfiber cloth. I would not recommend using any solution. Just a nice dry microfiber cloth should get it taken care of.
You do have to be precise though as around the edges you can grab little bits of left over adhesive and pull them across the screen and that will make big marks across it. Just use a little warm breath if need be and polish it as best as you can. Be careful also not to use too much pressure. Light and quick swirls are better than slow hard pushing.
Hope this helps