For a healthy young woman with no other immediate/anticipated healthcare needs other than preventive and birth control, a high-deductible with HSA plan has strong incentives. You did not post the difference in payroll contributions for the 2 choices of medical plans. But if you take that difference (you presumable pay much less for the HDHP option), plus the $600 that your employer is giving you in your HSA - I don't see how you could not come out ahead with the HDHP/HSA option. The choice to put in extra money of your own to fill out the HSA is wise so that you do have enough saved should something come up. Plus you reduce your taxable income by the amount you fund your HSA (and presumably your pretax payroll contributions for the premiums as well).
With regard to your specific Rx for BC - the above posters are correct. Generic birth control is covered 100% by all non-grandfathered health plans (this is a requirement of ACA) unless the company has claimed a religious exception (only recently, so unlikely that is your company). If you are paying $30/month - you must be getting a special brand name that is not preferred and could discuss with your doctor switching to another type/manufacturer that would be zero-copay. Also, if your company requires mail-order or 90 day refills and you are not doing that, that is another reason you may be paying out of pocket unnecessarily. Take your Rx id card out of your wallet and call the number on the back and ask the question of your pharmacy benefit provider. Or else - login to their online account if they have one and I bet they'll show you alternatives for the one you are taking that would be zero copay.