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You should include the amount shown on Form 1099-MISC (assuming the one reference to 1099-G was a typo) in income, as the IRS information return matching program will be looking for it. 

To enter a 1099-MISC for a legal settlement:

1. Sign in to TurboTax and open or continue your return.
2. Search for 1099-misc and select the Jump to link.
3. If you're asked Did you get a 1099-MISC?, answer Yes.
   • If you've already entered a 1099-MISC, select Add Another 1099-MISC.
4. Enter the information from your 1099-MISC and select Continue.
5. On the Describe the reason for this 1099-MISC screen,
   enter lawsuit settlement and select Continue.
6. On the Does one of these uncommon situations apply? screen, select This was money from a lawsuit settlement and then answer the back wages question before selecting Continue.

If, after reviewing the terms of your settlement, the information below, and information previously provided, you determine that part or all of the payment is nontaxable, make a second 1099-MISC entry in TurboTax, with an explanation, and enter the nontaxable amount as a negative number.

If the payment represented a settlement paid in order to return your property to the state it was in before the illegal actions, and to attorney fees paid attributable to that settlement, then it would be nontaxable. If a portion of the payment represented punitive damages, then that portion and any attorney fees attributable to that portion would be taxable.

From this IRS article on Tax Implications of Settlements and Judgments:

Treatment of Payments to Attorneys - IRC 6041 and 6045 state that when a payor makes a payment to an attorney for an award of attorney's fees in a settlement awarding a payment that is includable in the plaintiff's income, the payor must report the attorney's fees on separate information returns with the attorney and the plaintiff as payees. Therefore, Forms 1099-MISC and Forms W-2, as appropriate, must be filed and furnished with the plaintiff and the attorney as payee when attorney's fees are paid pursuant to a settlement agreement that provides for payments includable in the claimant's income, even though only one check may be issued for the attorney's fees.

Attorney fees and costs (including contingent fees) where the underlying recovery is included in gross income.

Unfortunately, attorney fees of this type are not deductible as miscellaneous deductions under current law. Current law only allows for the deduction of attorney fees and court costs paid to recover a judgment or settlement for a claim of unlawful discrimination under various provisions of federal, state, and local law on Schedule A. Business attorney fees may be deductible on Schedule C.