I think your question is extremely broad. Are you trying to put together a portable kit for your apartment or something?

Quite a few folks on here do pretty intensive stuff at home, so their "Home box" is basically a professional setup, just at their house.
For my home tools, I basically have a shop, HF 44", table saw, drill press, paint sprayer, air compressor(s), bench grinder, router table, ect.
If you're talking about what I call "kitchen tools", I have the following for the wife (and me when I don't want to go to the garage). All this is in a 15" Plastic Keter box we bought at Wally World, for less than $10.
Hammer
Tape measure
Arc joint pliers
Screwdriver set (including P3)
Adjustable wrench (big enough to change grill tank)
Wire cutters
Needle nose pliers
Slip joint pliers
Ball peen hammer (mini)
Wire strippers
Vise Grips
Pick and hook set
6 in 1 screwdriver
Putty knife
Strap wrench (great for cleaning shower heads)
Allen Wrenches
Hex bit screwdriver
Hex bit set
Mini level
Scissors
Calculator
Volt Meter
Outlet tester
Hex shank drill bits
Precision screwdrivers
Utility knife
Cordless screwdriver (B&D lithium ion, great tool!)
Consumables (teflon tape, zip ties, electrical tape, sandpaper, brad nails, general purpose glue, superglue, wire nuts, small screws, nuts and bolts, outlet cover screws
That's completely differnent from the shop, or my travel tools.