Sand Slime

It spawns in the Underground Desert on its own, with no summon, no event and no weather condition attached. Older versions put it out on surface sand during the day, which is why advice about walking the dunes still floats around. Ignore that. Drop into the sandstone caverns and you will meet plenty without trying.

Outside of Pinky, this has the best odds on a Slime Staff in the whole slime family, and the underground desert produces them steadily with no setup. If you want the minion before hardmode, this is where the hours go. A Water Candle and a Battle Potion help as they would anywhere, and the drop is still rare enough that you should settle in rather than expect it in the first twenty kills.

It hits about as hard as a Jungle Slime and carries the health to match, which is a nasty surprise on a first trip down while the rest of the desert is treating you gently. Royal Gel turns it passive outright and is worth the accessory slot for a long stay. It does not count toward Gelatin World Tour either, so do not tick it off that list.