modge podge is pretty much white glue. Its only a little thicker. For my costume I just used three - four coats of undiluted white glue, sand with 700 -900 grit sand paper (this you normally can't find in hardware stores, you'll need to go to hobby shops to pick up finer grit sandpaper.
Prime, sand again, then paint.
To answer you water question, PVA glue (which is modge podge, white glue etc.) Is water soluble so once you paint it, you will need to seal it. If it doesn't need to be flexible, clear coat it with an enamel or a varnish and your good to go. However if it does need to be flexible, you'll need a latex clear coat, and an umbrella.
I hope this helps.