First of all, unless your range hood vents to the outdoors, don't bother. Those that filter the air and blow it back into the kitchen are virtually useless.
For a new vent hood, your installation needs will dictate some of your choice. Most hoods can be installed several different ways (horizontal vent out the back, vertical vent out of the top, etc).
The power of the hood is usually measured in cubic feet per minute (cfm) of air moved. When shopping, compare cfm numbers. If you are quoted other power numbers such as watts (this hood has a 300 watt motor!), ask for the cfm. Depending on your stove, you may need more or less power. Regardless, you should look for a hood with 500-1000 cfm. More if you have a stove with high output burners, or more burners than the usual four, you may need more power.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan