It depends on how much the apartment costs, and what your other monthly expenses are, like say: if you have a car; how much food you eat; what you pay for entertainment; your insurance premiums, copays, and deductibles, etc. You also didn't state how many hours you work in a week. Are you part-time, full-time, or overtime? Full-time is usually defined as 40 hours per week.
Everyone's income-to-expenses ratio is different. I would recommend making a budget. I use a spreadsheet to manage my budget. Some people calculate their budget monthly; I prefer to calculate mine paycheck-to-paycheck since I don't make that much more than you. Two spreadsheet programs that I recommend would be Microsoft Excel or OpenOffice Calc (Calc is free and Excel is not, but Excel is more advanced).