Once an engine has been fired and run, a pattern is at least begun to set so parts should be reassembled in the same place they were removed. Push rods and rockers - you will probably get away without worry, but lifters - no

As Tech says, an organizer tray is great, but many (most?) folks don't do enough engines to justify having one. What I found works well for me is a block of scrap wood for the push rods, and rockers. Mine is about 14-18" long has 16, 5/16"-3/8" holes drilled most of the way through, in two rows of 8. Then there are 16 finish nails next to those holes where I "hang" the rockers and any other rocker hardware. Then for the lifters, I have another piece of scrap wood that I have used a Forstner drill bit and made 16 holes ~ an inch deep, again, in two rows of 8. Just don't do what I did last time and forget to number the holes tho in my case that time, it didn't hurt as the engine was a new never run crate motor. Another item that I have used as an organizer are egg cartons - but I find that they don't really work well unless you can find the older pressed paper kind - the new plastic kind tip too easily. Another I used - numbered plastic bags - which I use for lots of bits and pieces, regardless of where they come from if for no other reason but to keep all of the associated parts together for an assembly. And the last, and have used way in the past, which I do not recommend is a cardboard box where you just throw everything and hope for the best