Elmers will be fine as long as you stay away from the school glues which are more watery. I have been working my way through a gallon of Elmers Glue All since the Storm of Chaos. (I used about half of the gallon on 2 big projects and have been re-filling one of those small 7 oz. glue bottles ever since.)
I also use Aleene's Original Tacky Glue, which is faster drying, or at least I think it is.