I'm not sure where you've been shopping, but HDPE is really cheap on Ebay in comparison to other armour materials. If you're really struggling, you can even melt down plastic milk bottles and make your own HDPE sheet. I don't think I've ever seen polystyrol as a sheet, but my best guess is that it probably isn't good enough because I've never heard of it being used before.

As for batteries, mine is a 5s 3300mAh battery, rated for 65-130C discharge. My build is still in progress, but it's seemed adequate so far.