that battery dremel will work fine, You'll probably have to take a couple of battery breaks though. YOu don't want to run the dremel at full anyway otherwise it will melt the plexi, run it at it's lowest.
I don't think that there are different grades of plexi, thicknesses and types (plexiglass, acrylic (much clearer than plexi but easier scratched)....ect.)
Have someone help you when cutting the plexi. You cut they pour.