Definitely spend some time searching and remember that some apartments might not be run my major mangament firms. Where we are currently at is run by a smaller company and I have been very pleased!
I'm in Des Moines, Iowa and have found that some places that have all the amenities (pool, club house, gym, etc) can be expensive and poorly run. Not always but that just seems to be what I have come across.
I think the biggest thing to realize is that apartments are not built for the long hall-they are typically cheap and you will notice things as you look around- cheaper appliances, poor construction work etc.
Think of the positioning of your apartment- if it is on the north side you may get a cold winter breeze and pay more for heat.
Find out about the length of your rental agreement. Some require that once your agreement is up you sign another one immediately. Where we are is such a great deal- our year was up in November and if we want to leave we just have to give 30 days notice. We don't have to pay extra per month and we were not required to sign anothes lease. Find out too, heaven forbid, if you guys seperate or run into financial issues what it takes to get out of the rental agreement.
Another big thing I would suggest: Once you start your rental and get ready to move in thoroughly inspect your apartment, doors, appliances, the list goes on. Take note of everything and make sure your landlord is aware of any little issues- For example: Our fridge, bottom rack is plastic and has a crack in it. Sometimes those landlords can be shady and place the blame so make sure you document things..when you talk to them about what etc.
One more thing-people typically think..I want a super nice apartment etc etc Find a moderately price livable apartment- I can only assume you will want to buy a house at some point..don't overdo your apartment now and short yourself for your future house.