I had move to US on L1 visa on July 10 2009. I have stayed for 175 days by Dec 31 . With this my case is failing the substantial presence test. And went into non-resident alien. It is shy of 8 days to 183 days. I have been to US for a month in the year 2004. Can I make the first year choice?
If yes, then the Another question is that my wife and kid had stayed in US for 31 days by Dec 31 2009, can I claim the standard deductions.

Please suggest the correct way for filing the tax returns

Yes, you can make first year choice.
You will have to wait for over 4 months to file your tax return till you meet the Substantial Presence Test in 2010. Your U.S. Tax Return: Substantial Presence Test

You will get standard deduction of $11,400 and exemptions ($3,650 each) for both of you and the kid. You will also get child tax credit of $1,000 each.

You must both declare your worldwide income for 2009. If you have any foreign income, and on that income you paid taxes in the foreign country, then you can claim foreign tax credit (Form 1116) or you can use Foreign Earned Income Exclusion (Form 2555). Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income

You will complete forms W7 (application for ITIN) for your spouse and child and attach with your tax return. You can also deduct moving expenses. Use form 3903.

My Wife had stayed only for 31 days for the year 2009 so can I file jointly to get standard deduction

Yes, even when she has never been to the U.S.

I have used tax calculators and found that if I file as resident alien then I do get tax refund. Now as I will not complete the substanial presence test by April 15th and I don't have to pay any tax to IRS ,should I need to file for an extension for qualify the SPT test? What is the procedure to file ,if I take the first year choice and my SPT completes after April 15th?

Do your tax return, and do not file till you complete SPT. File Form 4846 for extension on or before April 15, 2010.

Are there any tax firms which can handle this kind of cases?