You might want to head over to the-digital-picture.com and read some of the reviews. Also keep in mind that if you want to test a lens, you can always rent the lenses you are considering before deciding which one to purchase.
All lenses have trade-offs -- which is why the camera allows you to swap lenses (you can swap to the lens which is best for your needs.)
"Zoom" simply means you can change the focal length within a range.
There are "wide angle zooms" (like the EF-S 10-22mm f/3.5-4.5) which has a range from wide to very wide.
There are standard zooms (like the EF-S 18-55mm f/3.5-5.6 which likely came with your camera if you bought the camera as a body + lens kit) which provides a little room in the wide angle plus a bit of telephoto focal length.
And then there are the telephoto-zooms (which go from moderately enlarged telephoto image to a more strongly enlarged telephoto image.)
I'm going to assume you probably want a "telephoto zoom".
A very common companion zoom lens in the consumer price range (priced to not break the bank) is the EF-S 55-250mm f/4-5.6 IS. I owned this lens and actually gave my copy away to a nephew -- I was never nuts about it. Mostly I found the contrast disappointing and the "sharpness" (detail resolving) was a bit soft & mushy. But some people really like the lens.
The EF 75-300mm (and there are a few) does not have an impressive reputation.. it's perhaps the least favorite lens in the lineup. The EF-S 55-250mm is a little better.
The EF 70-300mm f/4-5.6 IS USM has a fairly good reputation... it's a mid-range lens which means it's more expensive than the entry-level zooms.
That EF-S 55-250 has been updated to an "STM" version. STM is Canon's new "STepper Motor" technology. You can think of it as a "focus by wire" lens in that there is actually no mechanical linkage between the focus ring and the movement of the focusing elements inside the lens. Turning the focus ring simply sends input to the computer electronics -- and the electronics interpret and focus the lens.
But the lens has a few very positive things going for it:
The "MTF" scores for the lens are extremely good -- meaning that the contrast and resolution (accutance) of the lens seems to be greatly improved over it's predecessor.
The STM lenses are EXTREMELY quiet -- so quiet that it's hard to tell that the focus motor is even working. It was deliberately designed so that when shooting video, the internal mic on the camera would not be able to pick up the audio noise of the lens focus motor (on some lenses it can barely pick up the sound, but it is extremely quiet).
Lastly, the STM motors are not quite as fast at focusing as the USM motors, but they are much faster than the basic motors. So the STM version of the 55-250 will be a faster/snappier focusing lens than the non-STM version (which is a big plus if you are shooting action photography with rapidly changing focus distances.)
The list price on the STM version of the lens is only about $50 more than the non-STM version (about $299 vs $349 -- that's Canon list price... you may find retail stores selling it for slightly less.)
You can read a review of that lens here: http://www.the-digital-picture.com/Reviews/Canon-EF-S-55-250mm-f-4-5.6-IS-STM-Lens.aspx
I skipped comments on any of the "L" series lenses because they tend to be the most expensive lenses in the lineup (but offer the highest quality features -- not just in optics, but other features of the lens as well.)
I would probably take a very serious look at (in order of preference - best being first):
EF 70-300mm f/4-5.6 IS USM (on the spendier side so that may be out of your range)
EF-S 55-250mm f/4-4.5 IS STM (note the emphasis on "STM" and not the non-STM version)
EF-S 55-250mm f/4-5.6 IS II (not as good as the STM version but it will shave a few dollars off the price tag.)
EF 75-300mm f/4-5.6 III USM (in last place -- a mediocre quality lens, but it is the least expensive of all.)
Tim Campbell
5D III, 5D IV, 60Da
