Some scientists, museums and government bureaucrats, would discourage the hobby, but they are wrong. In the United States, meteorites are the property of the person upon whose land they fall or are found. If a meteorite is found on the federal lands, then government officials would consider it to belong to the government. Still, if you find a meteorite on your land or buy a meteorite from someone who found a meteorite on his land, or collect a meteorite with permission of the landowner, or buy it from anyone who has a legal right to it, then the meteorite is yours.
Some countries have laws that make it illegal to export meteorites.
For example, Namibian officials claim that it is illegal to export Gibeon meteorites. The operators of the Canyon Diablo Meteor Crater seem to discourage meteorite ownership. But in actuality, the owners of the crater have profited handsomely in the past by selling Canyon Diablo meteorites. Many of the specimens now on display or for sale can be traced to them. I would not worry about the ownership of this most common of display specimens.