I try to have LONG running forts, so I have to keep item count low -> hiding/ignoring the stuff is sadly not an option. My current approach seems to work nice so far:
1. There's some pretty damn big walled space outside my mine gate, that can be closed/opened with bridges from the inside. The bridges are usually open, I try hard to keep all the fighting within that space. When the fighting is over, I close the area, remove the civilian "stay inside" alert and let the dorfs collect the Goblinite.
Everything outside is designated "dbc" (collect) -> "dbd" (dump it all) -> "dbm" (melt items, overwrites dump, so items to melt go pretty straight to the Smelters. The active dump point is on the roof, and is designated as 1-tile refuse pile, so most of the stuff will rot away automatically (I really only want the metal). At that point, I cheat and dfhack the remaining items away - but an atom smasher would probably do exactly the same.
2. Cage traps. Animal stockpile is close to those roof stairs. One cage built right next to the stairs. All captives get assigned to that cage. dbc / dbd / dbm -> all non-metal items will be stripped and dumped (as above). When done - make ONLY ANOTHER dump point available. dbc / dbd again, all metal gets dumped there. When done, dbc/dbm on that pile -> off to smelters.
The now naked prisoners get pitted through a floor hatch into some danger zone - spike traps in the beginning, into the training barracks later, currently into the room with the 2 Hydras (they LIKE_FIGHTING). That room is drawbridge-sealed while this happens (Trolls and stuff, I only had a door first time, and the Trolls managed to destroy the door before the Hydras were done with them ...)
Once all invaders are dead, I open the bridge, and remains get hauled to Refuse pile. With the Dwarfen Higher Learning mod installed, my Hospital team makes good use of body parts to train stitching them up. Or, Atom smasher.
Generally, I try to win invasions by fighting them, but there's lots of cage traps between my military and the main fortress, in case somebody gets through in the heat of the battle.
Obviously, Cage traps are overpowered (Giant? gotcha. Cyclops? another Cyclops? a tameable Hydra? Dragon? All caught without without and dwarf getting into danger). So adjust to your playstyle, in my case I wanted to be foolproof on the surface because this is not the issue/goal of the current fortress.