When installing .dmg files what do you do?

So I've never had anyone show me how to do this. What I've been doing when I download a .dmg file is double-clicking them while they are in the "Downloads" folder. Then sometimes another window pops up shows a picture of like the app with an arrow pointing to the applications folder. So I've been then dragging the app over to that folder and then just close that window. But also in that windows is a Read Me file and something else ...I've just been leaving them and closing that window when the copy is complete.

Then after installing, I'll put the .dmg file in a folder in my Documents that I store all of them in and I'm backing up in case I ever had to reimage the machine I'll have all the .dmg files in one place.

Does this work, or should I be moving those .dmg files somewhere else prior to double-clicking on them? I would just like to keep everything nice and tidy so I don't have junk all over the place. But I also want things to run fast and I don't know if there's something I should be doing differently.

Anybody know the best practice or where I can look to read about it?