Yes, the IUD would work for you. Doctors now give IUDs to people regardless of if they have given birth or not. I can’t tell you which is better for you, it is definitely a personal decision between you and your doctor. The Mirena will last for up to 5 years, may reduce/eliminate your period, and protects you from pregnancy. The copper IUD can last up to 12 years, may make your period heavier, and protects from pregnancy.I would suggest doing a little research into the two to decide which will work best for your needs.
As far as price goes- they really aren’t that expensive. Although the upfront cost may be high it generally ends up being one of the cheaper options considering how long they last. Insurance also very often covers most it (it could even be free thanks to the Affordable Care Act). If you’re uninsured and want the Mirena, you can turn to the Arch Foundation who may be able to help you fund it.