I have visited Egypt three times and love the history.
I lived in the Middle East for five. years and understand its more recent history and struggle with terrorist and extremism.
Fortunately, the current leadership of Egypt has largely stabilized the country.
The country still has some risks, it is still a relatively poor country, despite its massive improvement in economic growth in the past 40 years. Security is still important.
I strongly recommend taking a group tour, that will have an armed security guard to protect the group. Renting a car and driving is NOT a good idea. Traffic is terrible and congested. Local drivers are aggressive. Public transport would be a bit crude by western standards and waste a lot of your time.
A Nile cruise from Luxor to Aswan or reverse is a very nice way to see southern Egypt. Also, recommend taking a tour that includes Abu Simbel in the far south.
Our last trip to Egypt was about three years ago and we used Gate 1 Travel. I compared six other comparable tour companies including Viking. Gate 1 was 60% of the cost of Viking. Our tour included airfare from JFK to Cairo and internal flights, hotels, most meals, tours, the cruise, transport, admissions, etc. Cost was no where near $10,000. The hotels were five star fantastic top hotels.
At least do your research checking Gate 1 as well as other tour companies. Also, if you plan to do stuff on your own, factor in costly taxis, admissions, etc.
You should know that there are areas of Cairo that tourist should NOT enter. The security of a group tour is important. When I visited Egypt the first time over 40 years ago, an Egyptian friend cautioned me on just taking a taxi. He said only take taxis where the hotel books for your and registers the name of the taxi company and driver. Apparently, some taxis would take tourists out into the desert, rob the tourist and sometimes other crimes.