Correct me if I'm wrong, but I am guessing you have a Canon Rebel "T6" camera. Not a "T6i", but a "T6" (no "i").
It is common for the series that includes the T6 to be sold in kit with two lenses. Usually those were an EF-S 18-55mm f/3.5-5.6 IS "II" and an EF 75-300mm f/4-5.6 "III".
Notice that neither lens has "STM" or "USM" designation. This means they use a slower, noisier "micro motor" to autofocus. This will make them less useful for action photos. They will struggle to lock onto and track moving subjects. The EF-S 18-55mm is okay in terms of image quality and has IS (Image Stabilization), but besides slower autofocus drive, it also has a fairly small maximum aperture and the front barrel rotates during focus and/or zoom. The smaller aperture limits how much you can blur down backgrounds in portraits while the rotating front barrel is a pain when trying to use a circular polarizing filter for a scenic shot. The smaller lens aperture (higher f/number) also effects focus performance.
It's even worse with the EF 75-300mm "III". That lens also uses a slower micro motor for autofocus. As a telephoto it probably is even more noticeable that it's not very fast focusing. Telephoto lenses typically have to move their focusing elements a lot farther than short focal length lenses. This lens also lacks IS. And, it doesn't have particularly good image quality... especially at the 300mm end of the zoom range.
Finally, the Rebel series viewfinders aren't the brightest. Lenses that stop down to f/5.6 like both of yours don't help with that.
There are definitely a lot of lenses that would be improvements for you. How much improvement depends upon your budget. One relatively low cost solution would be the EF-S 55-250mm f/4 (or f/3.5) to f/5.6 IS STM to replace the EF 75-300mm. The "STM" stands for "stepper motor" autofocusing, which is quieter, faster and smoother than the micro motor in your current lens. This 55-250mm also has IS, which is particularly helpful getting steady hand held shots with telephoto lenses. To buy it new, the current version of the EF-S 55-250mm costs $299 (also spend the $24 to get the ET-63 lens hood that's sold separately, then use it to protect the lens and make for better images. This lens also has better image quality than the EF 75-300mm III.
You can probably continue to use your EF-S 18-55mm for landscape shots. But for portraits, in particular, some have suggested the EF 50mm f/1.8 STM lens, which is quite affordable, too, and has a much larger lens aperture. It's more than a stop brighter than your EF-S 18-55mm (at 50mm). This means more than twice as much light to help AF performance as well as make your viewfinder brighter. While this lens doesn't have IS, it does have better performing STM focus drive. On a shorter focal length like this, especially with a brighter aperture that means faster shutter speeds, IS may not be all that important. Best of all, this lens brand new only costs $125. It has a fairly deeply recessed front element, so a lens hood might not be necessary. But if you want one, the ES-68 hood made for the lens costs $25.
An affordable lens that would "expand" your capabilities, especially for landscape photography, is the EF-S 10-18mm f/4.5-5.6 IS STM. Rather than duplicating or replacing focal lengths you already have, this gives you much wider angle of view, which is often popular when shooting landscapes, seascapes, cityscapes, etc. Among lenses of this type, the EF-S 10-18mm is compact, lightweight and one of the most affordable at $299 brand new, plus $25 for the EW-73C lens hood it uses.
If you want to try a circular polarizing filter to see what it can do for your landscape, etc. images in particular, the most logical lenses to use them on are the EF-S 10-18mm that uses a 67mm diameter filter and your EF-S 18-55mm that uses a 58mm diameter filter (and it uses an EW-60C lens hood, if you don't already have one).
Yes, there are even higher performance lenses available. But they are also a lot more expensive. For example, the EF-S 17-55mm f/2.8 IS USM is two full stops (4X) brighter than your 18-55mm, has top image quality, has IS and uses a "USM" or "ultrasonic" focusing motor that's even faster than STM. Another premium lens is the EF 70-200mm IS USM, where both f/4 and f/2.8 versions are available... 2X or 4X brighter than your 75-300mm. But, the 70-200s are pricey lenses too.
Since you are just getting started, try the EF-S 55-250mm IS STM lens. That will be your "go to" for equestrian action. Also consider the EF 50mm f/1.8 STM for portraits and the EF-S 10-18mm IS STM for landscapes/etc.
Besides the above lenses, you also might want to get a decent flash, an off-camera shoe cord and a flash. That can be useful shooting outside in strong midday sun, when shadows can be harsh. I don't use flash during the action shooting, but do use it at times for portraits.
Semi-back lit subjects... Canon 550EX flash (fill), EOS 10D camera, EF 70-200mm f/2.8 lens (at 160mm, f/5.6):
Overcast days and covered arenas have some advantages, but you need larger lens apertures to have fast enough shutter speeds. Beautiful light early and late in the day also can be ideal.
I've been shooting equestrian sports for many years. Everything from gymkhana to English/western, hunter/jumper to dressage. One tip I'll give you is to learn to use your camera's AI Servo focus mode in conjunction with Back Button Focusing. Also get in the habit of using a single point... the center one in your camera's array, which is higher performance than the other eight points. It will be on you to keep that point right where you want the camera and lens to focus. Don't leave it up to the camera to choose where to focus, by trying to use all the AF points.
Your camera can shoot bursts, but only at 3 frames/sec. My 7D Mark IIs shoot at 10 frames/sec and older models I have used did 8 or 6 fps. You'll need to carefully time your shots for the "peak moment" because you will probably only get one shot. I sometimes get two, three or more usable images in a short burst.
Even the occasional trail trials...
Throughout events, I keep my "head on a swivel" and an eye out for candid portraits & details...
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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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