By default, screenshots save to the Desktop which isn’t ideal. With this terminal command you can change the folder, e.g. to the Pictures folder:
defaults write com.apple.screencapture location ~/Pictures
To remove the setting and go back to the default do:
defaults delete com.apple.screencapture location
To query what the current setting is do:
defaults read com.apple.screencapture location
Here are all the key combos for taking screenshots:
command+shift+3 capture whole screen.
command+shift+4 capture drag to capture area.
command+shift+4 then space and click window to capture.
If you would prefer to use a simple menu bar utility for taking screenshots try my app ScreenshotMenu in the Mac App Store.