Ableton Live's Transport bar handles the basics of moving through your Arrangement view: Play, Stop, and Record. Play starts playback from wherever the insert marker sits, Stop halts it, and Record kicks off recording directly into the arrangement.
Clicking anywhere along the arrangement drops that flashing insert marker, letting you set your playback position instantly instead of dragging a playhead. It's a fast way to jump around a track while you're working.
One shortcut covers both directions: space bar starts playback and also stops it, so there's no need to reach for separate keys or click back and forth between Play and Stop.