Now comes the fun part: thinking inside the box. This is where the creativity and craftsmanship come into play. Your chest should be customized to your tools, your way of working, your tastes. My ideas and others you come across are suggestive only.
The lid. Many of these chests have nothing on the inside of the lid. If tools are stored there, it is most commonly saws. The argument against it is that some of the historical chests have damage because the hinges and supporting structure couldn't support the load. Admittedly that's an issue, but I just couldn't see leaving it unused because it is so convenient and accessible when the chest is open. I avoided the potential problem by using a 36" heavy duty stainless steel piano hinge installed with 36 screws into hard maple. It is very rugged and I haven't experienced any problems.
As you can see, I decided I would mount my saws under the lid and spent considerable time making secure ways to hold them. I custom shaped inserts for the handles, which look nice but I will have to redo them if I change saws. In use, I have found this a little cumbersome, though not bad. I think there is a better way though.
When I was looking at historical designs, I was intrigued by the Benjamin Seaton tool chest. I couldn't figure out how that saw till on the lid worked and that's why I went the route I did, but I think I may understand it now. Basically it looks like saws are slid into sleeves from the sides. They don't fall out because they are held in place by the sides of the box when the lid is closed. If I had it to do over again, this is what I would do. I also think that I would put my long handsaws elsewhere so I could have all of my other saws here. As it is, my Japanese saws, coping saw and fret saw have to be stored elsewhere. At some point I am going to rebuild the lid to accomplish this.
All in all, I think the decision to use the bottom of the lid for tool storage is a good one even if I didn't get it exactly right. I understand the concerns about the stress on the hinges but think I found a solution. Even if you don't like piano hinges, you can certainly find stout enough hinges and install them securely enough to avoid problems.
If you prefer to have your saws in a till, there are other possibilities for tool storage on the lid, limited only by your creativity.