Here are some key things you need to be aware of before signing a lease -
What is the landlord responsible for in terms of paying for utilities, and what are your responsibilities? This can get a little sticky, if your landlord wants you to pay for water, but it comes on the same bill as the garbage and sewer charges.
Pet deposit, or monthly fee? Sometimes this can be negotiated with your landlord, if they want you to pay and extra $50 per month for the duration of your lease. Ask if you can make an up-front refundable deposit if there is no damage at the time you move out.
Ask if they have ever had a problem with pests... if they say they don't know, etc., ask if they will take care of it if it develops and becomes a problem. And GET IT IN WRITING. Everything you ask for should always be put in writing and signed and dated by both you and the landlord.
Ask that the carpets and or unit in general be professionally cleaned before you move in. This isn't being a Diva - this is basic courtesy, and it's surprising how many landlords don't do this.
Ask (if you are so inclined) for a reduction in rent if you are willing to do grounds keeping - mowing the yard, keeping up flower gardens etc. Be sure to specify exactly what your responsibilities are though too - you each might have different definitions of "grounds keeping. Oh, and GET IT IN WRITING.
Last but not least - READ your lease very carefully before you sign it. Every word. And ask questions to clarify anything you don't understand. This seems like a no-brainer, but so many people just sign on the dotted line, and then regret it later!