Ah, the pesky non-hormonal birth control question. I struggle with this on a regular basis. Last time I was on the Pill (after having been on the patch) was a low point in my life and relationship with my (then newlywed) husband. I don't think I tolerate hormones well either. One day I just stopped taking the Pill, and it's amazing how much better things have been since.
I used LadyComp for awhile after that (it's a computerized thermometer basically, which predicts your fertility using basal body temperature only), and then got pregnant on what I think was a "yellow" (use caution) day when I ovulated earlier in a cycle than I normally do, though we knew we weren't being perfectly "safe." I don't really blame the device, but I do think its predictive powers are iffy when your cycle is as irregular as mine was in those days (some 45+ day cycles; even a 50+ day cycle, but never regular and often anovulatory). One of the bigger problems with it was we got so few "green" days (safe days); ideally, as it learns your cycle you get more "safe" days, but it can get frustrating when almost all month is "yellow" (learning your cycle/use caution) or "red" (high fertility) days. I have a friend who used the cheaper version of this device, Pearly, successfully for several years, and if I had to do it over again, I'd buy Pearly rather than LadyComp, which I paid more for because I was told I wouldn't have to send it in to get the battery replaced (it turns out this is not the case; although you can recharge the battery on LadyComp, once the rechargeable battery loses its ability to hold a charge, you still have to return it and pay for a new one; Pearly's battery is not rechargeable and needs to be replaced every so often). I think FAM has some of the same drawbacks as LadyComp/Pearly, but if you can be well disciplined either method is a good option.
After this baby was born my midwife suggested NuvaRing, but I wasn't willing to go on hormonal birth control again, especially while breastfeeding. We've been using a combination of withdrawal (very occasionally), outercourse, and FAM. I'm not great about charting, especially with a co-sleeping, nursing toddler, but I am working on it, and I love the more intimate knowledge it gives me about my body's cycles. I monitor basal temperature (as best I can), cervical fluid/mucus, and cervical position, and I use an online fertility program (I've tried both FertilityFriend and the website associated with Taking Charge of Your Fertility--TCOYF) to track my cycles. I also highly recommend Toni Weschler's book; I own a copy and it's an invaluable resource.
I think since you're planning to TTC in a few months, FAM would be a good choice for you. I don't think it's a great option if an "oops" baby would be devastating, especially if you're just learning how to do it; in our case, we'd be fine if we had another pregnancy (especially now that DS is over 20 months old), so I feel pretty comfortable using it. My cycles post-pregnancy, once they returned at 9 months postpartum, have also been more regular and that helps a lot. We've been considering getting a diaphragm too, but I haven't used one before, so I can't recommend it one way or another.
If you are going to try FAM, I would highly recommend taking vaginal rather than oral temperatures--you want to be consistent within a cycle (so don't start temping vaginally if you've been temping orally until the start of a new cycle), but I've noticed much more regular temps once I switched from oral to vaginal (I think I'm a bit of a mouth breather at night, especially in cold and flu season).