When looking at apartments make sure you know how much you can afford and stick to your budget.
Rent an apartment that you can easily afford the monthly rent payments on. A nicer apartment is a nice thing to have but not if you'll be spending most of your income on the apartment rent and having to eat Ramen Noodles for example.
You don't want to have no money left over after paying for rent. Rent an apartment that is safe but also below your means.
Check the amenities as well and decide on the ones that are a must have and ones that are just nice to have.
If you don't have to have it then don't go with the apartment that costs more just for the extra amenities.
Ask current tenants what they think of the landlord and apartments to get an idea on how the place is to live at.
Make sure you go through the apartment and inspect it to make sure everything in the apartment is working and if not pass it up and go find another apartment.
Also be aware of any scams that may be lurking around such as on craigslist. If the deal sounds too good to be true then it probably is.