"12-speed Shimano SIS".

Check out how your derailleur attaches to your frame. Most frames have an arm that extends downward from the dropout that the derailleur bolts onto. Some frames require a "claw" on the derailleur that attches to the axle.

If your frame has the arm, and you buggered your derailleur with a plastic bag, your derailleur hanger alignment is probably buggered too. It needs to point straight down. On a bike with a 6-speed freewheel, you should be able to eyeball it straight enough so it will index. Be sure that you have a derailleur bolted onto the hanger before bending it or you might ovalize the derailleur mounting hole.

Most modern Shimano derailleurs will index with your shifters. Short cage is fine. If you're on the economy plan, I wouldn't worry about trying a used one.