So long as your business does not have any W-2 employees, just make the payment on line and make sure to print your receipt and file it with your 2018 business records. NOw if your state taxes personal income, you'll need to pay your state quarterly taxes too. Not all states offer the option to pay online though.
As for your business expenses, and other stuff, don't worry about dealing with it until tax filing time. But I do urge and highly encourage you to keep finely detailed records of every penny in and every penny out of your business. There's three rules to always keep in mind when dealing with the IRS.
1) You are guilty until proven innocent.
2) The burden of proof is on the accused (that would be you!) and not the accuser.
3) If it's not in writing, then it did not occur.
