I suggest using Excel, unless or until you reach a point where Excel is inadequate.
Here's a possible setup: an Excel workbook with a sheet for each person or item being tracked. The first tab could be for the Electra, another for Amelia, one for Paul Mantz, for George Putnam, etc.
Each column is a day. So the sheet for the Electra would have a column for August 2, 1936, and you would note there that on that day Earhart and McLeod flew to Mills Field. The column for August 18 would show that the Bureau of Air Commerce issued the aircraft a license as R16020.
The sheets for Earhart, Bo McNeely, and everyone else would contain all that you know about their whereabouts and activities each day, along with photos, maps, and links.
Excel can store text, graphics, and hyperlinks. You can also link to another location in the workbook.
One big advantage of using Excel: you can start today. (I'm presuming TIGHAR has a copy of MS Office.) You don't need to evaluate, purchase, and install specialty software to get started.
If you use Excel and eventually decide that you need some functionality that Excel doesn't have, you'll be in a better position to choose a product. You'll know exactly what you need to do that Excel won't do, and you can evaluate products with that in mind.