Can I play Long Sword into base and not equip it to anything?

No — you cannot play Long Sword and choose to leave it unattached if you control any unit on the board.

The Quick-Draw keyword says "When you play this, attach it to a unit you control" — this is a mandatory triggered ability, not optional. If there's at least one friendly unit on the battlefield, the trigger must target one and attach the Long Sword to it. You can't hold it back in reserve at your base.

The only way Long Sword remains unattached after being played is if you control no units at all — in that case the triggered ability can't finalize (no legal target), and the gear stays at your base.

Once it's attached and later becomes unattached (e.g., the unit dies), you'd need to pay the Equip cost to reattach it later — Quick-Draw only covers the initial play.