Hi and welcome! You will surely enjoy your time here... Palermo is lovely, I live in Soho. I have been here just over a year and have lived everywhere from Colegiales to Puerto Madero. To answer your questions...
First, you should understand in order to rent as a foreigner, short-term, in Palermo, you will be paying significantly more than the locals or you would in other neighborhoods. For a "reasonably sized" one bedroom (not a studio) I would expect to pay somewhere between $750 and $1200 USD/month. Also, keep in mind, Palermo is a VERY large neighborhood with many subsidararies. You have Palermo, Palermo Chico, Soho, Hollywood, etc. Many places will claim Palermo when in reality they are in Colegiales or the border of Abasto. The following sites should be useful for you;
mapa.buenosaires.gov.ar - an interactive map to show you the exact location.
The following sites are a bit more expensive, but worth the price. They charge a nominal service/administration fee (around $40USD) and everything is included from maid service to taxes, city fees, etc.
Good Luck and Happy Hunting!