Best rear derailleur for a Schwinn ranger?
Any Shimano rear derailleur designed for 7 speed (3 front x 7 rear gears =  21 speed) drivetrains and mountain bike gearing will work.

For your practical purposes, the compatibility chart from Shimano below gives part numbers for the available rear derailleurs which will work with a 7 speed MTB drivetrain: 



Those part numbers can be specifically matched for each derailleur.

To break down the part number I will use RD-M360 as an example.

"RD" = Rear Derailleur - "M" = Mountain Bike - "360" = model ID number
"RD" = Rear Derailleur - "TX" = Touring Bike - "800" = model ID number


Typically, the higher the model ID number, the better quality the part.