Woman/Mom here.
If she's nursing and the idea of becoming pregnant again right now terrifies the heck out of her (as it did me), she should look into a progestin-only BC. IIRC, the estrogen-containing options can affect milk supply. Otherwise, don't be shocked if you end up with Irish twins. Nursing suppresses the menstrual cycle, so you can't rely on having a period as "evidence" you aren't pregnant while nursing.
Post-nursing, have her check out Nuva-Ring. I have several friends who like Mirena (and other similar IUDs), but Nuva-Ring has been great for me. No side effects whatsoever, and it keeps your cycle extremely predictable/regular. Leaving it in for the "placebo week" will allow her to skip a period (which can be convenient if going on vacation or something like that).
The thing about these hormones that a lot of people don't understand is, while yes, you are putting "extra" hormones in your body, these are hormones a woman's body produces naturally. But the body is terrible at producing them consistently...which is why so many women really suffer during their cycle (cramps, mood swings, irritability, nausea, erratic/heavy flow, etc). The beauty of modern science is we don't have to suffer anymore. Hormones in and of themselves are not bad, especially at a low dose. The problems associated with a woman's fertility cycles are not something that "living a health lifestyle", eating right, and exercising can fully address.
If your wife is in otherwise good health, doesn't smoke, has not previously been diagnosed with cancer, and is not prone to or have a family history of blood clots, then a low-dose BC should not have any negative side effects (the wrong/too high of a dose will). It just might take some trial and error to figure out which one is best.
Also, educate yourselves on the two main types of hormones used in BC (progestin vs estrogen) and how they work in combo vs alone. There is a difference, and that difference may affect her choice on whether to use one or the other.