I've tried trays which swing off the column, magnets, pegboard, but the best solution for me are the Kennedy #520 7-drawer machinist's chests. They can sometimes be found for $25-50 at yard sales.
Position one by each drill press, lathe, mill, surface plate work station. Holds drills, indexes, punches, hole saws, scribes, rules, squares, calipers, micrometers, dial indicators, lathe bits, mill tooling, clamps, taps, dies et al.
jack vines
I've tried trays which swing off the column, magnets, pegboard, but the best solution for me are the Kennedy #520 7-drawer machinist's chests. They can sometimes be found for $25-50 at yard sales.
Position one by each drill press, lathe, mill, surface plate work station. Holds drills, indexes, punches, hole saws, scribes, rules, squares, calipers, micrometers, dial indicators, lathe bits, mill tooling, clamps, taps, dies et al.
jack vines
Sound advise except for the tools that jump from box to box at night and when you go to grab one its always across the room in a different box.
lg
no neat sig line
exactly why I have the dupe set at the DP! It saves a lot of this: 
If you have the room I would suggest a small table or a cabinet hanging on the wall within reach vs the press tray. My setup.... small table that holds fixtures, blocks of wood, and chuck key. Also doubles as a place to stack parts when doing multiple pcs. And the bit cabinet to hold everything nice and clean and easy to see.
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what Is it called and where did you get it?
I use the same tray as Chad for my most frequently used bits. It's very handy but it doesn't have the strength/space for a full index.
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It clears the handle folded in or can be swung out, as in pic#2
I use the same tray as Chad for my most frequently used bits. It's very handy but it doesn't have the strength/space for a full index.
I have one of those bolt on trays like Chad posted. It's OK I guess but I'm not all that thrilled with it. I do not leave bits in and use it more as a shelf to temporary hold bits or small parts while working at the DP.
My issues with it are A. It's very light duty and I wouldn't expect to it to hold much weight and be (and maybe this is just mine) but the tray does not sit level so **** rolls around on it and sometimes off of it.
Always found those trays too large and got in the way.
My solution....
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It clears the handle folded in or can be swung out, as in pic#2
That's a good idea!

I have a drill press tray like Chad's above but I replaced the tray with a 3"x3"x12" block of Oak. It's hard to see in the picture below but I simply drilled holes in it to store drill bits, chucks, centre punches, etc. Most of my tools for "making holes" are stored in the tool cabinet under my shop press.
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Yes it is hard to see, I'm not seeing it at all!![]()
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You'll have to use your imagination. When I took the photo the purpose wasn't to highlight the "empty" wood block.Looks like a 3X3 block for storing your chuck key in!![]()