Very welcome, glad I could help. The "sport" setting is one of many settings somewhere in between full manual and full auto. As long as you understand why/how they are modifying the auto settings, they are great to use. Sport is expecting outdoors, lots of natural light, and fast movement with no flash. So it is going to use a really fast shutter speed to freeze fast moving cars, dogs, or sports players without flash. This often means the F/stop is sacrificed (very short depth of field, see how behind dog is blurry). This all works very well for what you want to do - not use the factory flash, short depth of field, fast shutter. If this was an overcast day, the camera would likely have taken very dark pictures because of that short shutter speed and no flash or slightly grainy/blurred pictures.
Hundreds of shots is great. Invest in figuring out how to "filter" the camera's OEM software now. Usually there is some sort of preview method where you can go through a slideshow full screen really quickly and hit a certain key to keep the good ones and go through hundreds of pictures in a minute.
For the F stop, you want to find a shutter speed that works for the dog (usually 1/500 or 1/1000 for full lighting) that freezes the motion. The longer the shutter speed (more light let in) the better up until you get blurring, unless you are looking for that effect. Leave yourself a little buffer room in case he puts on a burst. Now from this point, let him take a two second break and focus (auto focus is fine) on his eyeball. Snap a shot and adjust the F stop so that his entire body is in focus but not much else by adjusting F stop (depth of field). Now take some pics with those settings. ISO is generally referred to as quality of photo. The cloud cover will determine this because you are using no flash and a very short shutter, so the lower (closer to ISO100 or IS050 whatever your camera has) the more small detail the photos will have. Start around ISO800 on that camera and go as low as you can go without having to adjust your F stop or shutter speed. Now a few test pics...too bright? If on lowest ISO (best quality), either expand the depth of field or go even faster on the shutter. Too dark and you're at your highest acceptable ISO? You're going to have to slow the shutter and only shoot when he looks 3/4 speed or so or shrink the DOF. Portrait style colors will probably be best to bring out his natural reds and browns and take emphasis away from the blues and greens in backgrounds. I would (always) be on continual shoot mode. Auto focus, and select the center dot only as focus point. This allows you to follow his motion as he runs, put dead center on his eye then move to compose quick and bam bam bam 3 shots. If you don't select a specific dot the camera is going to (slowly) figure out which one it thinks is best and you may end up getting a foot-focused shot.
Keep in mind that if you shoot in RAW mode it does take a bit more time editing because you have to when done convert to JPG but it allows you to edit nearly anything so long as at the moment of shooting you have the shutter speed, DOF, and ISO correct. (Yes, you can darken or lighten the image and effectively edit shutter speed but it greatly sacrifices quality).
You did great on composition (angle, height, focus, body position, etc) and that is a great first steps, you are leaps and bounds ahead of most. This takes many students years to develop this "photographic eye." Especially with people or animals, when in doubt, GET CLOSER. I cannot stress this enough. You can never get too close.
Those are all pointers relative to this type of shooting and will vary with subject/circumstance. I would advise start going through all the menus of the camera and get familiar with the main functions on the body of the camera (buttons). As in, what does color palates do, what is the lowest ISO quality I can stand in a final pic, what do the cloudy/sunny/overcast settings do. Then figure out which mode you prefer most - shutter priority or aperture-priority (these are half manual, half auto). Most photographers spend their time on these modes for non-portrait or full-setup (studio) work. Figure out if you are more comfortable manipulating the F stop and letting the camera do the shutter speed based on that, or manipulating the shutter speed and letting the camera do the F stop in different situations. This will give you nearly full manual control without the need to have hundreds of throw aways in editing because you were full manual with 2 variables.
If you are doing any of this to possibly print, keep in mind your camera and your computer screen are back lit and therefore images appear brighter than when printed on professional paper and front-lit. So you need to do some sample shooting and intentionally leave your images edited 1 to 2 shutter speeds faster than look good on the screen or camera. It will end up looking flooded out of color on screen and good in print. (for internet, just upload, we're all viewing backlit).
