Best way to organize and rebuild old sets?

So I have a huge bin of LEGO bricks that are taken apart from a ton of sets I had in my childhood. I built them, took them apart to build my own things, and now they've been in an enormous storage bin for years. My parents are cleaning stuff out of their house to reduce clutter, and I've been meaning to pick up the LEGO bin. I really want to reassemble all the really cool sets I used to have, but I'm unsure how best to do it. I know the LEGO website has all of the instruction books for free, and I remember the majority of the sets I used to have, so that isn't a problem. But my issue is figuring out how to get started. I'm considering getting large gallon ziploc bags, looking at the list of pieces in the back of each manual, and sifting through the bins to find each piece for each set. At the moment I don't have a strong desire to create my own builds, I really just want to have and display the sets I had as a kid, so I don't think I need to sort by type of piece or something. Is my plan of action probably the best one?