Range on most frequencies you'll be listening to depends, in part, on height above local ground (IOW, distance to the antenna's "horizon"). Outside your basement - on the ground - the antenna's horizon is a few dozen feet or so. *From 150MHz and up, most signals travel in straight lines, so if your antenna can't "see" the transmitting antenna, you'll get a very weak signal at best.)
The ground plane, if the antenna is on a decent ground (not all places "on the ground" are good grounds) you don't need a metallic ground plane. If you do need one, silver is best, copper next, etc. (The more electrically conductive the better.) Ferrous metal (basically iron) is a poor substitute for copper, but on a car it's usually the only choice you have.
As far as stubby antennas:
1) Shorter range.
2) More convenient if you're moving a lot. (You don't stab yourself in the ribs with the end of the antenna,)
3) People who are "radio-illiterate" think they "look better", or that they're supposed to use them, or some other reason that's a few light years removed from reality.