There is some work for you to do. You have to go back to all your corporation's record, books, bank statements, accounting records, and tax returns.
It is a very detailed work but probably is not difficult.
Go back as far as possible, year 1, the best.
You want to make sure that these are earnings of the company. Then, you take long-term capital gain, dividend, qualified dividend, on your tax return. It should be on your 2014 tax return, its tax rate is based on your other items on your tax return.
It is also possible funds your father loaned the company, he borrowed from banks, etc. This could be his original investment into the company. Then, taking them out is not a taxable event. This could be his wages he already reported income tax on his tax return. A lot of business owners issue wages to themselves but never withdraw from the bank because they don't need the cash at that time. Or they need to keep the money to make the cash flow for that period of time. Then, later on, they forgot about it. You need to reconcile all the wage the corporation issue to him and how much he actually taken out from the bank as wages.
You want to check the characteristics of every dollar of this 250,000. Think it this way, every dollar you can find that is not an accumulated earning in the company is tax free amount. Verify and keep complete, and good records.
Eventually, you need to close down this company. If you take on the basis your father have on the company when he passed away, and compare it when you close down, you may have some minor loss.
As to your question about how to pay the tax authorities, apply for installment payment plans. Hopefully, because it is long term capital gain, the total tax is not too great.
Please feel free to follow up.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP