The best thing would be to e-file them both together. The reason is that under the new requirements you are only able to e-file them both together or mail them both. When you e-file, will know if/when your Federal e-file is accepted (much quicker than filing by mail) and then you will still have until April 18th to pay it to avoid interest and penalty. Paying your balance due can be easily completed on the IRS website and if for some reason you are unable to pay your balance due, the IRS will also consider payment arrangements. Please see the IRS links below for more information:

https://www.irs.gov/payments

https://www.irs.gov/individuals/online-payment-agreement-application

(edited 03.20.17)