Hi Terry,
Welcome to Laptop GPS World.
This is a very nice idea. I think any PC GPS navigation software can do at least some of it. Most programs provide distance to destination and ETA, but I'm not sure how to provide ETA for the final destination and also ETA for the next rest stop, both at the same time.
I think I would first attempt to integrate into this project
Microsoft Streets and Trips. The reason being is that the map looks very nice. There is a free 60-dat trial download of the fully functional program.
The hardware is the easy part. when you decide on the mapping software, you may just buy a bundle that includes a GPS unit. It will save you money, and you will avoid potential compatibility issues. Alternatively, you may buy one of many USB or Bluetooth GPS receivers. They cost about $40 to $60.