If you want to know your natural cycles, I'd recommend using FAM/NFP, which is charting to avoid pregnancy. When you're ready to TTC, you can just use those charts to help you get pregnant. I'd recommend reading Taking Charge of Your Fertility and the Fertility Friend tutorials (you can get there through any of the chart links in our siggys). You can still use a barrier method during the fertile window, but charting will help you identify when that is.
I don't know that I'd go from BC to relying only on that if you've never done it before...unless you are 100% OK with getting pregnant while learning what your fertile window is.
I know you and your SO don't like condoms, but you woudn't be using them for very long.