Re: Your ideal Star Trek memorabilia...
TNG: How about those various alternate universe comm badges that Worf wore as he flipped from universe to universe. Just having a set of the original comm badges would be neat and portable.
TOS: Kirk's chair. I'd swivel mount it and use it in front of my computer. Heck, maybe I would even have one of the TOS desks and put my laptop on it.
Judy Waxhorn: "Lighbulb is shot can't see a damn thing. Prepare to trash the ship. LaForge, disable the warp-core protection system. Troi, take the helm. All hands, prepare for DRAMA."