Carnations and mums last the longest.You have to change the water often make sure the vase is very clean each time. Hydrangeas are great because if you cut them and put them you can dry them without water and have them forever.
In my experience, tropical flowers last the longest of all cut flowers. Bird of Paradise, gingers, heliconias are some that have a long life after being cut. Anthiriums also do really well and can last weeks.
Carnations last the longest, usually staying fresh and beautiful for atleast a week or two. Plus, they are available in lots of colors, sizes and varieties!
I have tried many cut flowers in my home and have found that astromenia last over 2 weeks with minimum care. They come in all colors and are really beautiful.