My most used home handyman tools (concrete building apartment, in no particular order), which I'm considering minimal.

• Safety glasses (must have!)
  
• Compact hammer drill (corded, variable speed) + bits
  
• Ryoba saw - amazing performance on wood/plastic
  
• Hot glue gun + glue sticks
  
• Combination square (with bubble level and steel ruler).
  
• Utility knife + blades
  
• Hammer (good to have 2 - one with rubber/plastic head)
  
• Cordless screwdriver + screw/nut bits (compact, not drill like, but powerful) can be used without a battery too.
  
• Portable worklight (DIY, 110V/12V)
  
• Pliers (2 pair minimum, large and small)

Supplies always at hands

• Box of Fix All
  
• Duct tape/Electrical tape
  
• Assorted screws, nails, washers, and bolts and nuts.
  
• Assorted sandpaper
  
• Stiff steel wire
  
• Soft electrical wire
  
• Pieces of 2x4 wood (~ 4 ft long)
  
• Pieces of plywood (~ 4 sq.ft)

Notes

• I'm using my soldering iron quite often too, but that's if you are good enough with electronics (eg wiling to fix a torn charger cord). Add a multimeter then.
• For my many hobbies the Dremel tool +attachments is a fantastic do it all tool, but it's probably have an unjustified price tag (especially with all bits and attachments). Add wise grips.
• If you are into basic plumbing you might have to consider some specific tools (most notably large wrenches and sealing supplies). Ah, I see it was covered above.
• As mentioned above a good long extension cord is very handy. Just don't be fooled by Christmas lights cords.