I'm in agreement that it's just about impossible for me to narrow the choice down to three items. But it's safe to say these three are among my best. As this is an ordnance forum, I'll choose two that are grenade related but allow me to slip one gun in to the mix.
The submachine gun in the upper part of the display is a Hyde-Inland M2 and was part of a display two of us put together for our annual gun collectors club show a few months ago. Most of the data on this piece can be read on the display card, but in brief, it was adopted to replace the M1A1 and other Thompsons and was itself replaced by the M3 grease gun just a year later after only 400 were produced.
I know of only one outside the U.S. in the former Pattern Room collection and just two in private hands over here. It's live and functional although I haven't fired it often as spare parts are nonexistant if something breaks.
Next is the Babbitt sling grenade I posted a couple photos of here in August. It now sports a reproduction firing pin and hood assembly and is more or less complete, although the streamers are pretty rough. I regard this as one of the scarcest of U.S. service grenades as they were only issued for about 7 years and never in combat, as near as I can determine.
Most American grenade collectors would probably consider the Civil War era Haines Excelsior to be the most rare and desirable hand grenade with sales values of existing samples known to exceed $10,000. And no, I don't own one of them but sure wish I did. At the gun show mentioned earlier, two other collectors were present that own 7 Haines grenades between them! Neither had ever seen or heard of another Babbitt.
Last is the Panzerwurfmine 1(L), my favorite German stick grenade. I have a thing for personal hand thrown anti-tank grenades like this, the Russian RKG-3, RPG-43, and even the factory produced Molotov cocktails. They seem to convey the incredible bravery, desperation, or perhaps insanity of soldiers who go up against a tank single handed with just a grenade to stop it. No standoff distance, fancy rocket launchers, tungsten or DU penetrators fired safely from shielded artillery, just run up and kill a 30 ton armored vehicle all by yourself.