Electricity and gas bills just turn up with the old occupants name on them, so provided you pay them on time you dont need to change the name on the bills with any urgency. You can pay in cash as pago facil etc. If you wanted to pay through the bank you would need to make the change.
With internet etc, I use telecentro and pay monthly direct debit using my UK credit card. I think the telephone companies (telefonica and telecom) and more difficult to set up.
As soon as you have completed your purchase you will need to find a local person to represent you with AFIP, if the property is worth over 305,000 pesos you need to pay asset tax, and only a resident can administer this, so you will need someone who is willing to do this. If you are not going to be in Argentina permenantly the AFIP will assume you are renting and you will need to pay tax on this rent. They will check electricity consumption to see whether the apartment has been occupied whilst you were out of the country. Failure to pay taxes can result in fines and penalty interest a 3% per month. Also you will not be allowed to sell until AFIP are happy that your taxes are in order.