Book well in advance, and unless you are adventurous choose a formal tour. You can go cheaper on your own, but the better tour packages provide help in negotiating Egyptian bureaucracy, hotel snags, unfamiliar traditions and language.
Most travel agencies can offer you tour options, but for direct information--or if you prefer to design your own tour--contact the Egyptian Tourist Authority, 630 Fifth Ave., New York 10111, phone (212) 246-6960.
Be sure to ask about the following: (1) Traveling from Cairo south or vice versa via the new, air-conditioned sleeper train. It's inexpensive, comfortable, travels by night and saves money on meals and hotel. (2) Riverboat tours on the Nile. Relatively moderate prices include meals, tours, plus swimming pool, air conditioning, etc. (Good buy--eight days on the Nile Princess, $450 per person in a double, much less in summer). (3) Red Sea beach resort at Hurghada for fishing, snorkeling.
If you're going via Israel, be aware of VIP Travel, the agency that pioneered Israeli travel to Egypt. Excellent connections and knowledge of Egypt touring peculiarities. Ask about bus trip between Egypt from Israel. It takes a full day, involves delays at the border, but is exotic, comfortable, cheap ($25 one-way, starting from either country) and offers excellent views of the Sinai and Suez Canal.
Shopping is great for linens, copper, carpets, alabaster. Don't rush it: wait, watch, learn, reserve time for unhurried buying. Good bet is Aswan, where you'll find high quality, good prices, and less-annoying hucksterism and haggling. Generally, Egyptians are friendly, helpful, fond of Americans.