My hair is definitely not naturally bright red. I had to bleach and color my hair red to achieve the color that I wanted. And to be honest, I'm actually really pleased with the color of my hair (even though my family isn't), the only thing that I don't like is that it's hard to maintain. Colored hair, especially vibrantly colored hair, is extremely very hard to maintain.
Expect to be buying a lot of fancy shampoos that are safe for colored hair. Also, arctic fox and color depositing hair conditioners are going to be your best friend. Depending on how often you wash your hair and how vibrant you want your hair to be, you're going to be touching up your locks quite a lot. The biggest secret to having nicely dyed hair is that you need to maintain it. Your hair will become your baby and you're going to have to attend to it like you would a baby.
Having dyed hair is expensive. A list of items that I've bought to maintain my hair includes (but is not limited to): hair oil, fancy shampoo, arctic fox, deep conditioners, nourishing masks, etc. So expect to be spending a lot of time, effort, and money on your hair. Also, expect all of your towels to get stained. Also, expect the collars of your shirts to get stained. And also your pillows and bedsheets. Basically, expect everything to get stained.
In short, dyed hair is really great. But it's a big commitment. So if you're going to dye your hair a color that's not brown or black, expect to put in a lot of work. What you put in is what you're going to get back, so all of your hard work will not go unnoticed.
Good luck and I hope this helps in having the hair of your dreams!