Cobwhip

Landing a hit drops a spider that goes off and fights on its own. It takes no minion slot and it follows none of the rules your summons do: it ignores the target you flagged, it picks up nothing from your other whips, and it chases whatever happens to be nearest. Treat it as a patch of automatic damage you leave behind rather than as part of your lineup.

Whipping faster does not build a swarm. A hit while one is already out just resets its clock, so the rhythm is to tag your target, let it work, and spend the rest of your time on an actual weapon instead of mashing the whip. Its armor penetration is the sneaky part. Before hardmode the enemies that shrug off your damage are the ones with defense rather than health, and the spider goes straight through it.

The living loom version of the recipe is the convenient one, because a living tree is already where a new summoner is headed. If you are standing at the loom you are usually a few blocks from the chest that holds the starter summon staff, so the trip pays for itself twice.