A good general rule of thumb is no more than one third of your income. However, every person's monthly budget is different. If your income fluctuates, one third might be too much. If you have substantial fixed monthly debt payments such as student loans, credit cards, car loans or leases, etc. one third might also be too much. Also be sure to get a sense of what the monthly electricity/heat and any other fixed costs associated with renting any apartment. If you are moving to a new area and will be commuting to work, make sure you factor in any extra transportation costs that you don't have to pay now.
The most important thing is to try to keep the rent and all other associated costs that you don't have now low enough that you can still save for your future. Good luck.