PS: If you apply for citizenship will need to "prove" that you have an honest means of living. If you are going to be living off your saving for a couple years I suggest that you have a CPA or bank officer write a letter (with the letterhead of the bank) to verify the existence of the funds and how you can access them when you are in Argentina;.
You might consider opening a trust account which is linked to your savings/checking account from which you can make ATM withdraws in Argentina. The funds could be invested in CD's that mature in 90 days, six months, or one year and are automatically deposited into your personal account.
This might also be acceptable to migraciones if you want to apply for temporary residency. The monthly income you would have to receive is currently $30.000 pesos. (about $2000 USD). If this is savings that you earned before getting temporary residency you should not have to pay income tax on those funds in Argentina, and as long as you are a only a temporary resident, you don't have to declare those funds or pay the bienes personales tax on them. As migraciones will want "proof" that you can meet the income requirement for temporary residency, you would need to have two years of available funds (about $50,000) in savings to get the visa rentista or pensionado.
If you do not have the required documents of the Rentista Visa (property lease/rental contract, bank verification of payments, etc.) and proof of official retirement (Pensionado), you will not qualify for either of these residency categories.
You might (probably would) have to deposit another $25,000 USD when you renew the visa (at least the first time). Once your Social Security income begins you can include that instead of making a deposit for the second and third renewals of your temporary residency, but at that point you might as well go for citizenship if (based on what the lawyer tells you) you did not apply for citizenship in the first place
It might be helpful to bring your latest "statement" from Social Security that shows how much your monthly benefits will be, but it probably won't carry the same weight in the court that grants citizenship as an official benefits letter that you will only be able to get after you start receiving monthly payments. The annual statement from Social Security that projects future benefits will be 100% useless at migraciones.
if you apply for residency at migraciones you will need the FBI report that is less than 90 days old when you submit the paperwork.
If you apply for citizenship you will need to show your "honest means" of income and copies of your passport. If your first visit to Argentina was in a previous passport I suggest you also bring it, but the court will no doubt check with migraciones to verify the date of your first entry. The court will also ask for a certificado de domiclio which of course you will get here. You won't need to get an FBI report until/unless the court asks for it.