The concrete porch on the front of my home, as well as the attached steps have sunk, and the posts that go to the roof ar no longer attached at the bottom. It's a small porch and roof, extending 5 or 6 feet out. There is a small step down from the house onto the porch. The concrete porch is cracked. I'm wondering if it would look better and be more cost effective to have a wooden porch built over the existing concrete, as opposed to have the porch lifted. I have an extremely limited budget.

Wood resting on the existing concrete sounds not to be feasible if that is what you mean.
Maybe if you could provide some photos someone might have an idea but it doesn't sound very promising from your description. The concrete would have to be removed I believe as it sounds as if it will eventually collapse and could damage the bearing points of any wooden structure built independently over it. If the budget is that limited, maybe total removal of the porch and roof and replacement with wooden steps with railing only might be the only option and would certainly make a safer situation than it sounds like exists now.
Some churches have groups willing to tackle projects like this. Best of luck to you.

I bought my house in May this year, and just last week discovered that the front steps and railings (which we never use) made of PT are built over concrete. The steps themselves are gone. There is no overhang.

I would call two carpenters to give ideas and quotes. I think you could cover the concrete porch, lift the posts and put new supports under them, and just remove the concrete stairs and build wood ones.

Jobs are getting scarce for carpenters about now if you are in the north, so this is a good time.