That photo was taken with a Nikon D3000, so a pretty entry level DSLR. I normally shoot with a Nikon D80. The Nikon D3000 is Ginta's camera. We have a DSLR each as we are both keen photographers and would otherwise be arguing over who get to use the camera and when. Apart from the Nikons we also have a Lumix TZ35. This is a replacement for a TZ10 which we accidentally dropped. We use the Lumix when we dont want to carry the heavier cameras. We find the Lumix range to be very good for our purposes
When it comes to taking photos when we are on the move, we tend to grab whichever camera happens to be closest to hand. Why? Because most photo opportunities are fleeting. A few seconds of fumbling around for the right camera, messing around with settings and whatever and the opportunity is gone.
With regards to taking photos, the final image is a combination of the subject, maybe action/movement, and light, and the angle of the shot. Yes, there is an element of luck - everything needs to be lined up to create the opportunity, but you also need to see the image and recognise it for what it is. Its about seeing light and the effects of light rather than just than just the subject itself. Sometimes the light changes before you take the photo and you wait for ages for the opportunity to recreate itself, and sometimes it does and sometimes it doesnt. And if it does, it is rarely the same image, the light might be different, the subject (or you) might have moved, something might have entered the frame, you might even frame it differently. And yes, you do need the technical equipment, and the equipment does play a significant part, but remember early photographers took some pretty impressive photos with some very basic (analogue) equipment, and each film subsequently at the mercy of the processing lab.
I think there is a lot of good (and some not so good) kit out there today, and that ultimately you need to decide what you want it for, your price range and how comfortable it feels to you when you are handling it. Then, whatever you chose, it is a question of getting as familiar as you can with the camera through practice, so you can take photos efficiently with the least fumbling and messing around.