I have shot cars at the track with the T7 and EF-S 55-250. Works great for panning.
Mountain landscapes can be shot with the EF-S 18-55mm lens you got with the camera. (Some day you might want to get a good quality "circular polarizing" filter that fits this lens... it can be very useful when shooting landscapes.)
Animals such as pets can be photographed with that lens or a telephoto we'll suggest below.
Animals such as wildlife typically require longer telephoto lenses.
Motorsports also usually require telephoto lenses from moderate to long, depending upon the facility, how fast the action is and how close you can get to it.
In addition to focal length, autofocus performance is another concern. Not so much with mountains, but with active pets and wildlife as well as motorsports AF needs to be fast to keep up with the action. The faster the better!
Canon uses three basic types of autofocus drive systems. From slowest to fastest they are micro motor, STM and USM. (STM = stepper motor. USM = ultrasonic motor). Lenses that use micro motor don't have STM or USM imprinted on them, while lenses that use either of the two faster focusing drive systems are always imprinted with the type.
As far as I know, there has only ever been one Canon lens that came in versions using all three types of focus drive: the EF-S 18-135mm. Canon claims the USM version of that lens is 2X to 4X faster focusing than the STM version (note, this particular lens also introduced a more advanced "Nano USM"). I don't know how much faster the STM lens is than the first, micro motor version of that lens, but am sure there's a significant difference.
Finally, another feature to look for in Canon lenses is IS or "image stabilization". Your EF-S 18-55mm lens has IS. It's great to have on any lens, but is particularly helpful on longer telephoto focal lengths. Shooting rapid action with faster shutter speeds may not demand IS, but it can be helpful when doing a lot of other stuff including panning shots like those in that other response.
Several responses have recommended the EF-S 55-250mm IS STM lens and that's a good suggestion you can buy new within your budget.
Because it has USM and a little longer telephoto reach, the Canon EF 70-300mm IS USM would be even better. But the "II" version bought new costs $599. If you would consider used, you might be able to find a good example of the first version close to your budget.
There also is an older lens called EF 70-300mm "DO" IS USM. This was a special lens that uses "diffractive optics" to be very compact (but not really any lighter than the other 70-300s). When it was new, it was the most expensive Canon 70-300mm... even more than their "L" series "pro" version. I found a couple examples of this lens selling on MPB.com for a little more than your budget. Might be worth a look! A friend of mine used this lens a lot and she made great photos with it!
You also might be able to find a good used EF 70-300mm IS USM "first version" for close to your budget. It's a little bigger than the "DO" but about the same weight. And it's quite capable, too.
With your limited budget, those are probably your best three possibilities... good performing lenses for your purposes. If you consider used, besides MPB.com there also are KEH.com, Usedphotopro.com (Roberts Photo), and used departments at Adorama and B&H Photo. All of these are reliable. Another place to look is the Canon USA website, refurbished lenses.
Whatever you get, I strongly recommend always using the matching lens hood. It's sold separately, but sometimes included when buying used). Each lens uses a specific lens hood, which also can be reversed for storage on the lens. Lens hoods not only make for better images by shielding the lens from stray light, they also help protect the lens from bumps.
Finally, shooting active animals and motorsports you will need to set your camera's focus to "AI Servo" and I recommend Single Point using just the center AF point of the AF array. That's a more sensitive and faster working AF point. I don't think these settings can be used in full Auto+ (green box) or the "scene modes" such as "Sports", "Landscape", "Portrait". I think you will need to use one of the "Creative Zone" settings, as Canon calls them: Av, Tv, P or M. The first three are auto exposure, but allow you to select other things like focus setups. M is "manual".
Some motorsports examples (since that appears to be your primary concern).
This panning shot was done with a 70-200mm f/2.8 IS USM lens at 90mm, f/16, on Canon 50D at 1/100 shutter speed (ISO 100)...
On my 2nd 50D I was using an EF 300mm f/4 IS USM lens and a faster shutter speed to freeze the action. I used f/5.6 aperture to blur the background a bit, ISO 400 and 1/3200 shutter speed.
Access to the track at Laguna Seca for the historic races is very limited. There are fences in the way with some "windows" cut in them to shoot through. But this makes panning shots pretty much impossible. For this shot I was using the same EF 300mm f/4 IS USM lens as above on a 50D, f/5.6 aperture, ISO 400, 1/1600 shutter speed.
I added a 1.4X teleconverter to the same EF 300mm f/4 IS USM lens for a tighter shot, effective 420mm focal length, f/5.6 aperture, ISO 200, 1/1600 shutter speed.
The first couple shots above (autocross) were shot hand held. I used a monopod for the 3rd and 4th shots (historic races).
In the paddock at the historic races you can get a lot closer to the cars, I could use my 135mm...
Or even 12-24mm lens...
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Alan Myers
San Jose, Calif., USA
"Walk softly and carry a big lens."
GEAR: 5DII, 7DII (x2), 7D(x2), EOS M5, some other cameras, various lenses & accessories
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