I have a Canon Rebel T3i. I have the standard lens. I am looking to buy a telephoto lens that won't break the bank! I am looking at a Canon 55-250 telephoto lens. Is this a good quality lens,and will it fit the T3i?
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 cameras with the EOS-M mount, but (with an adapter) an EF-M camera 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.
Answering the title: no! As others wrote, EF and EF-S lenses will fit the crop-sensor DSLRs; only EF will fit the full-frame DSLRs.
Here's the "no" part: older manual focus lenses use the FD mount, which will not fit on Canon's autofocus cameras; only the manual focus cameras.
On a aps-c camera ef and ef-s lenses will fit. Vintage FD lenses can be put on with a passive adapter for macro work. However, to focus to infinity yo need an adapter with a lens and that type of conversion is not a good idea.
On a full frame camera ef lenses will fit. FD might work, but FF cameras often have physical trouble with the mirror action with vintage converted lenses.
On a EF-M camera you can use EF-M lenses and ef and efs with adapter. you can even get an official canon adapter. EF-M lenses doesnt convert well to ef and efs - it would need the lens type (havent seen them around either).
Ef and efs on FD camera with adapter (without lens) should be possible, but since they have no manual aperture ring there isnt a market for it.
Is this a good quality lens ?
I use this lens (the latest IS STM version) on a 1200D and I am very happy with the quality. It is my daughter's favorite lens, it leads to a details-oriented style of photography that is much unlike my own style. Definitely worth buying (the lens, not my daughter).
I happen to agree with this guy: https://kenrockwell.com/canon/lenses/55-250mm-stm.htm . It's plasticky, handle with care.