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I recently a acquired a large, good quality, black shoe box - black inside and out (came free, with the new shoes  ) that can be pressed into use for the trickiest disassembly. I use the inverted lid as a tray but the box itself, with good high sides, when disassembling anything for the first time that might contain unexpected 'exploding parts', which could make a bid for freedom.

I also have a large white-moulded Melamine tray with a nice curved lip surround that makes things like washers easy to slide up over the edge and into my hand.

Finally, I use a range of translucent boxes with snap on lids* for disassembly and storage of part disassembled/re-assembled cars so the correct parts are kept together.

(*The sort you get with microwaveable meals from the supermarket, for example.)

For anything ferrous that DOES get away - a 'magnet on a stick' works well - and if using a torch I shine it across the carpet's surface to throw the item into relief.