If you don't want to be on hormones (which is what I'm gathering from your post), Mirena isn't for you. It has progestin in it (bcp and nuvaring are a combo of estrogen and progestin). Depo is just a shot of progestin (no estrogen).
Paragard does not have hormones.
I'd discuss with your doctor the risks/advantages of having an IUD. I was offered one several years ago because I had to be off of estrogen for a time. I turned it down for a variety of reasons.
IUDs are excellent for long term birth control, but some women have problems with them (cramps, prolonged bleeding). Some think they are awesome (no need to worry about a pill, sometimes no periods either). The upfront cost is high (but lower overall in the end over pills). It's easy to "undo" when you're ready to get pregnant, but it does require an office visit.
Just some things to think about.