Birth control

I recently started having sex, ive been abstinent for all 22 years of my life. My partner doesnt like to use condoms and honeslty ive never wanted to use one either. My bf does have an issue, he was diagnosed with low sperm count. Him and his last partner were actually trying to concieve for 5 years and they couldnt. We are currently just using the pullout metgod, i looked into the calender method and it seems really simple. My cycles are regular and i have an app that predicts ovulation  amd fertility. Does anyone else use these two methods? How effective are they?
Does anyone else have a partner with low sperm count? If what do you use for birth control?