Over the years on different trips we have travelled around Egypt by Bus/Train, self-drive rental car (Cairo - Abu Simbel return plus Sinai) and "Cruise". The most recent (the "cruise") was 2 years ago but conditions change. If you spend time perusing the Lonely Planet Forum you should pick up the latest info on many of the subjects you are interested in http://www.lonelyplanet.com/thorntree/index.jspa
(either select Egypt and go from there or use search limiting key words like "Egypt Car Rental")
You are wanting to fit in a lot over a fairly short time - a problem with public transport is that the logistics of travel can "waste" time. It is all very well for someone on the forum who is travelling for weeks/months to say how wonderful it is! For instance even all those years ago one couldn't guarantee getting a ticket on the night sleeper Cairo-Luxor the next day! And 3rd class "stop-everywhere" trains will use up your days.
The end of the convoy system nearly everywhere will have made self drive "easier" - We didn't find the police a problem as in some countries where getting hassled at checkpoints or for fictional misdemeanours gets very wearing. It is nice to be able to take the quieter roads on the "other" side of the Nile and it is a lot easier to pick up locations like Beni Hassan, Armarna. The car has all the advantages of flexibility , ease of trying different hotels before deciding etc etc. Downsides of course are the possibility of accidents, traffic (A rental car is a liability in Cairo - but I am glad I have done it!). With the cost split 3 ways and if you are confident with driving in such conditions it would probably be my preferred choice for travel. Actually the roads are not bad and, as I remember it (despite concerns in the Thorn Tree), all significant signs were in English as well as Arabic - though knowing the Arabic numerals for roadside distance markers helps - but this is easy enough and is worth having anyway.
the "Nile cruise" in my opinion is over-rated. The Luxor-Aswan stretch isn't very long and a lot of time is spent with the boat tied up alongside a dozen others with a "corridor" through all the boats -add the lock wait at Esna and some overnight travel then you don't see a lot of "The Nile Banks" anyway -if you want that experience i would think of a shorter day return trip from Luxor (there is a regular one whose details I can't remember e.g is it every day or not -- you will probably find it on the Web somewhere or in LP) or a Felucca.
Crowds at the sites are a massive problem in Egypt now - being on your "own" has its advantages and disadvantages - can you avoid the large groups or thread your way through or will you just get pushed to one side? Both will happen! I think that a good case could be made out for a "first time" visitor to Egypt to take an all-inclusive package and see the main sites with a guide -going back on another trip to see things by themselves together with the less common sites. From UK they are remarkably cheap. In much of the world a guide is of doubtful use but, despite myself, I have to say that they can add a lot to a visit to an Egyptian site - unless you are not particularly interested in the detail. On the other hand being stuck with a bad one or one whose approach doesn't "please" could be hell!
I have never felt "at risk" in Egypt. Hassled yes but no worse. Obviously all "normal" care should be taken
Re hotels -the only time we had any problem was in non-tourist towns between Cairo and Luxor - eg Assyut where the choice was limited because most tourists don't overnight there. Luxor, Aswan and Cairo have plenty of choice and we found 2* acceptable. But things can change re availability depending on world economic circumstances and time of year. If it is very important to you to have a guaranteed clean room then you have to travel and pay accordingly! A lot of 4* hotels in Luxor are geared to groups - whether that means they have knock down prices for empty rooms I don't know. Re prebooking - possibly for Cairo on arrival? It depends on your time of arrival - I personally don't like having to look for hotels after a long flight and at 2 in the morning! If you like the hotel you can probably stay longer and also book for the last night. Cairo is enormous and travel very slow unless you can use the Metro (though even "Giza" metro station is 10kms/20mins from the pyramids!) so there is an issue re best location which you will have to decide - out at the pyramids or city centre. Given that you want to visit other aspects of Cairo I would probably go for the city. I don't have a particular recommendation.
Finally - it IS "touristy" and someone did get killed (!!) the other month but I would recommend the balloon flight at Luxor - shop around for prices as always. We used Sindbad which was ok and we got a good deal despite buying it at the desk in the Winter Palace Hotel! We must have got the "special rates" for "last minute" as per this Web site E£300 @ UK£1 = E£11 http://www.sindbadballoons.com/Rates.html