For fit:
Short answer: YES. 
Longer answer: Each camera has a type of mount and is part of its specifications. All modern Rebels (yours included), XXD (60D/70D/etc), and 7D cameras are EF-S mounts. Full frame cameras, such as the 1D/5D/6D series use the EF mount. The EOS-M uses the EF-M mount. An EF-S mount camera can use an EF or EF-S lens, but an EF mount camera can only use an EF lens. EF-M lenses can only be used on the EOS-M mount, but (with an adapter) an EF-M mount can use EF and EF-S lenses. As others have pointed out, there are some older mounts that have limited or no compatibility.

For quality: you get what you pay for. It is the cheapest lens I can think of for its range and comes with trade-offs. The aperture is not as wide as others, isn't as sharp, but is cheaper and more lightweight than any other lens like it. For a beginner, it's not a bad way to go.