It's preferable to have a stand that does not touch the hot part of the iron for the simple reason so that the stand doesn't get hot and burn you. You're overthinking the tip cooling aspect, otherwise. The vast majority of proper iron holders have the tool pointed downwards in a pencil grip type of arrangement, supported around the part of the iron where one would grip it. This allows for better stability and ease of insertion and removal.
Unfortunately when buying a holder for an existing iron it's a bit of a tossup on whether or not it will fit well, so YMMV. Consider investing in a proper soldering station (Hakko, JBC, Pace, Metcal, etc) that comes with a matching set, at some point if you do enough soldering
