Suggestions: 1. Before taking the shot, isolate what you wish to capture with your mind and eye. Zoom (if possible) or move until you have what you consider to be the focal point (not focus point). Post shooting, crop where necessary to capture only the important elements, use phone, camera or computer software.
2. Less is usually more when "composing" your "great shot." If you get home, look at the shot and wonder why you took the shot, it's not a great shot.
3. See the "great" part before activating the shutter.
4. Focus! If your subject isn't sharp. it ain't a great shot.
There's more, much more that comes with having a critical eye. And, I'll readily admit, "great shots" is always subjective. But, "snap shots"/interesting shots do not equate to "great shots" with respect to what the OP was asking for.
An aside: The OP used shots he found on the interweb. My preference is shots the members worked for. Show the results of your hard work and eye. Put some effort into it and this could be a worthwhile collection, improving constantly over time.
There skilled shooters here who, I suspect if asked, would be happy to critique and offer suggestions.