Absolutely! Egypt is a destination filled with historical treasures, vibrant culture, and beautiful coastlines. Here are some tips for your travel:

Best Time to Visit:
The best time to visit Egypt is during the winter (December-February) when the weather is milder. However, this is also the peak tourist season, so attractions can be crowded.

Route and Accessibility:
Your trip could start with Cairo, where you can visit the Great Pyramids of Giza. To travel to Luxor, you can take a domestic flight, or overnight train. From Luxor, a short flight or a bus ride will get you to Hurghada on the Red Sea coast.

Altitude and Acclimatization:
Egypt is fairly low-lying, the highest point being Mount Catherine in the Sinai Peninsula. Thus, altitude sickness is not a concern here.

Accommodation and Booking:
Hotels of all price ranges are available in all three locations. Booking in advance is recommended, especially during the peak tourist season.

Clothing and Essentials:
Given the hot, arid climate of Egypt, light, breathable clothing is essential, along with a hat and sunblock for protection against the sun. However, remember to dress conservatively to respect local customs, especially when visiting religious sites.

Health and Safety:
Keep a bottle of water with you at all times to stay hydrated. Only drink bottled or treated water. Be aware that tap water is not safe to drink in Egypt.

Local Etiquette and Respect:
Dress modestly and respect the local customs. When visiting religious sites, women are often required to cover their hair, shoulders and legs, and men must wear long pants. Egyptians are generally very friendly, but be aware of scams and touts, especially around tourist sites.

Lastly, don't forget to try the local cuisine and enjoy your trip to the fullest. Egypt is a beautiful country with a rich cultural heritage.