Patio Furniture and Sod

I don't know about the patio furniture, so I can't help you there.

Here in Texas sod (we're also re-doing our backyard!) is around $80-$90 per square 100 yards. I would not recommend you doing it yourself, unless you know what you are doing. If sod isn't put down correctly, on healthy soil...you'll lose it anyway. We are re-doing our sod this spring, but my farther is an arborist, horticulturist, and landscape expert. One thing I will mention, is that in warmer climates, the sod will take to the ground better at the very beginning of spring. I have SO much info on this, but I came across a really great how-to with tons of information.
http://www.thisoldhouse.com/toh/article/0,,###-###-####,0...

P.S.
Buy your sod from a nursery, or landscaping business...NOT a home improvement store.

Target carries nice patio furniture and they carry stuff that you can fold up for winter (small bistro sets).

I would talk to your landlord about the sod. Maybe he/she will pay for it or half since you will be adding value to the home. You should be able to purchase it from home depot or lowes. You need to be sure to get rid of any weeds and clear the area before putting it down.

Check out second hand furniture stores. And big box stores.

As far as sod goes I would contact home improvment stores. You could also rent a tiller and till the soil in the backyard and put down grass seed. I think it would be more cost effective. You will need to get a lawnmower and cut the grass also.