I've done a couple cycles off bc and a couple on and honestly, thought the results were comparable. I know the higher level competitors do go off the pill because of the estrogen so as to limit the amount in their body, which yes, helps in getting to those lower level body fat, stage ready levels. Logically, it makes sense to go off of it for that reason but for me, the impact was minimal AND it takes my hormones 3-6 months to even out, especially as you get older. I just got tired of messing around with that. I know I'll never compete at a national level so it's not worth the few months of hormonal disaster.
I don't believe tapering will do much for you and wouldn't bother with that either. In terms of sides, it's so individual. Some women lose their periods on 5 mgs/day of var, so it's tough to answer that question. I honestly don't think bc will limit your gains to any great extent but that's just my opinion. If you train hard and have your diet in check, you'll see some good gains.