In any scene, there is a finite amount of light available to your camera. You choose how much of that light is exposed to the sensor by changing the aperture, shutter speed, and ISO.
Each of those three controls can be changed to increase or decrease the exposure, and each control also has a different effect on the image: depth-of-field from aperture, motion blur from shutter speed, noise from ISO.
Getting a properly exposed photo requires balancing trade-offs. You can reduce the aperture size (higher f-numbers) to increase your DOF, but doing so reduces your exposure, so you have to increase the shutter speed (and motion blur) or the ISO (and the noise) to compensate (or some combination of the two). If you don't want any motion blur, you can choose a high shutter speed, but doing so reduces your exposure, so you have to increase the aperture size (lower f-numbers, lower DOF) or increase the ISO (and the noise) to compensate.
This sounds tough, but fortunately your camera has a light meter, and a manual that tells you how to use it. There are also endless resources online related to exposure and the relationship between aperture, shutter speed, and ISO.
The reason your "sports mode" photos come out okay is because it's one of the camera's auto modes, and it is automatically adjusting all three of those variables to obtain results that would generally be good for sports photography. It also processes the image using preset values for contrast, saturation, sharpness, etc. which are also tuned for sports photography. I wouldn't call it a "no-no", but if you use it, learn to look at the EXIF data on the photos, which will tell you what aperture, shutter speed, and ISO the camera chose for you, and then compare that to the EXIF data where you chose those values yourself, and you will be able to see the difference.
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