Heads is the correct term, and yes, they make a biiiig difference! Have the heads on it ever been replaced? If not, I highly recommend you go out and pick up new top/bottom (proper term is "batter" and "resonant") heads for each drum ASAP :) Hopefully one of you can tune drums, but even if not, Bob Gatzen and many other dudes have great tuning videos on YouTube.
As for selection: first, you need to measure each drum's diameter (not including the hoop- basically, measure from the inside of the hoop on the top of the drum to the other side) to figure out what sizes the kit is. Common sizes are 10", 12", 13", 14", 16", 20", and 22". As for selection, it probably doesn't matter what brand you go with, so here's a little table to help:
For batter tom and kick heads, basically choose a clear head if you want more attack/clear pitch, or coated if you want more of a thump/smooth tone.