IUD? Birth Control options in Catholic-dominated healthcare system?

J.
Due to my age (37) and history of stroke in my family, I've never been on birth control. Until this year, I've never had an unexpected pregnancy either lol. In my area it's all Catholic healthcare. In order to obtain birth control, I will probably have to go to a different gyno 30+ minutes away. Anyone have experience with IUD or other non hormonal birth control? I will not take the pill or depo shot.