A few things to realize before renting an apartment here is that they do NOT always include appliance such as hot water heaters, refrigerators and stoves and sometimes they do not even include light fixtures. That will vary from apt to apt, but do not be surprised.
You are generally liable to return the apartment in the condition in which it was rented, meaning you are not only liable for normal wear and tear, but also for things that are not always your fault like a leaky pipe or running toilet.
There are arbitrios it is a property tax. there are also property taxes. Generally the landlord must pay the regular property taxes but the arbitrios, which is really more for city services is generally paid by the renter, not always but usually. Find out what they are, but they are generally cheap, less than $150 a year and sometimes cheaper if you pay the year in advance.
As far as Chi Chi's advice, while his comments on apartments in this case is right on, his other comments omits thing you might find important.
Riders and workers on Public Transportation report a higher than average problems with asthma and respritory illness. More people, per capita, are killed or injured on public transportation and bus lines in Peru than in any other Latin American country and crime on public transport is higher than in many other countries. I am not saying it is unridable as I use it myself quite often, but do not confuse what Chi Chi says to think it is always a pleasant option.
There is a thread here about the cost of living in Peru that you will find very helpful. I am afraid it is long and has several off-topic tangents, but if you take the time, I am sure you will find most of your questions answered there. viewtopic.php?f=1&t=94
You need to set your budget as to how much you want to spend on an apartment instead of figure out what the local prices are, then hunt accordingly. You can find things in miraflores and san isidro for anywhere between 350-2000 USD a month
Just a little ways away, you can go to Surquillo and find it much less and Surquillo has good streets and bad streets, so you need to sort of shop around.
other areas you can consider could include barranco, San Borja, and Santiago de Surco without moving too far out of the way. Those are generally considered safer areas and prices vary according to specific area. There are tons of temporary flats that range from 400 - 700 USD a month in Miraflores right where you will be working. If you go a little farther out, you can lower that.
With the ranges I listed above, the majority will be closer to the middle. I would say an average 1 bedroom apartment in miraflores or san isidro is 550 dollars more or less, surquillo 400 dollars more or less. If you are willing to live a little farther or in an in-between area you could probably save some money, if you want an ocean view, you best be prepared to look at the 700-1500 range.
If you are willing to commute, you could save more money on housing with a compromise of commuting time and costs and a certain level of safety though there are many moderate neighborhood that are not unsafe.
Someone could easily come along and offer you figures that differ from mine, some will be higher, besides chi chi, not many will be lower.
I have a friend who rents small furnished flats in San Borja for $400 a month that are safe and reliable, but from where you will be working, it would require 2 buses or about 10 Soles in Taxi to get there and during rush hour, about 35 minutes. If you are interested, send me a private message.