If you are already receiving the monthly income indicated, you can immediately apply for residency. Please refer to my posts on residency and the DNI for more information. Does your user name "justarrived" mean that you are already here?
If you come/came here with all of the necessary docs you can have them translated and legalized in about a week. Meanwhile, you can get an Argentine criminal report. Then all you have to do is go to migraciones and submit the papers. If they are all "in order" you will be told to return in less than 30 days and you will be issued your "residencia precaria" which you will then take (along with another copy of your passport, birth certificate, and a certificado de domicilo which costs 10 pesos) to the registro de las personas to apply for the DNI.
If you do not speak castellano it would be wise to have a native speaker go with you when you apply for the resident visa. It does not have to be a lawyer. I can (highly) recommend someone if it is necessary. It is NOT necesary to speak more than a couple phraes of castellano when applying for or renewing the DNI. You can do this on your own.
Once you have the residency from immigration there is a 100% certainty you will be issued the DNI. It will bear the date that you were granted residency, so you might have to renew it a lot sooner than you were expecting. The renewal process is EASY, takes a couple hours, and costs $45 pesos!
Once you have the DNI you will be elligible for domestic air fares which are about 50% less than charged to non residents. You will also have no trouble opening a bank account and you can renew the visa annually without leaving the country.
The cost of the resident visa is 600 pesos per year. You will spend between 1000 and 2000 pesos for the translations, depending on how many pages you have (it's just simple math). The Argentine police report costs 40-60 pesos.
If you have the resources and desire to buy an apartment, you can do so at anytime (even with just the tourist visa), but with the residencia precaria you will be able to transfer as much money as you like without the 30% hold by the national bank on the amount over the "stated" price of the property. Just be sure you can show that the money was legally earned. It is also very important to have the residency and DNI when selling property here.
It is still possible to buy a nice, remodeled, front facing, two bedroom apartment in Recoleta for $200,000 but at this price they are rare. I do know of one at the moment. (No, I am not in the real estate business.) Add about 8% to the purchase price for closing costs (real estate agent's commission, escribano, and money transfer fees).
My best advice is to rent a furnished "temporary" apartment for one to six months and see how you like living here. I came in May of 2006 and rented in Palermo for six months. Then I bought an apartment in Recoleta. I have not regretted it for a nanosecond.
If you have any questions, please post them here or send me a note.
Remember, utilities and property taxes are low here and if you don't have a car, you will not be spending nearly as much on a monthly basis as you would living in the US.