You can apply for an installment agreement with the IRS to set up a payment plan. I recommend using the online installment agreement application with the IRS directly rather than filing Form 9465. The fees for setting up the plan are cheaper and you get an immediate response on your agreement.
https://www.irs.gov/payments/online-payment-agreement-application
As for penalties, you generally are going to be charged a small penalty for failure to pay your tax on time along with interest when you have an installment agreement. But, the penalty is only 0.25% on a monthly basis when you file on time and have a payment plan. The larger penalties are when you fail to file a return and don't pay taxes by due date. Its possible you could qualify for penalty relief if you have "reasonable cause" or meet the requirements for the first time penalty abatement for not paying on time, but note that interest will not be abated for reasonable cause - the IRS is statutorily required to charge interest. You can apply for abatement via a written letter or calling the number on your IRS notice (you should eventually receive a notice concerning the penalties that will have a specific number or you can preemptively call the IRS at 800.829.1040).
Here are a couple of links to check out for penalties and possible relief -
https://www.irs.gov/businesses/small-businesses-self-employed/penalties-at-a-glance
https://www.irs.gov/businesses/small-businesses-self-employed/penalty-relief-due-to-reasonable-cause
