Israel is a beautiful place to visit, and I recommend everyone should go.
If your traveling alone a rental car is almost a must if you plan to see as many sights as you can.
Drink lots of water. It tends to be very hot in Israel and your will do a lot of walking/hiking.
If you want to float in the Dead Sea make sure you don't get the water in your eyes because it will sting very badly. If you do happen to get the water from the Dead Sea in your eyes simply take some fresh clean water and pure it over your eyes to wash away the Dead Sea water.