What I did in my situation was simply cover up the existing concrete porch with pressure treated (pt) lumber. The existing porch was 4í by 4í, and uncovered. I wanted basically 6í by 10í, with a roof. Since my porch had steps leading up to it, and since each step was made with a 2x6 for the form, I power-nailed a 2x6 pt to the face of the top step, and attached joist hangers to it. The power-nailer I am referring to is a gun-like device that uses a 22 caliber charge to fire a single nail through hard material such as metal or concrete. You can rent them at tool rental places, or buy one. The bottom-of-the-line model is under $20, and I have used it more than enough to warrant itís price. If you decide to use one, READ AND FOLLOW ALL CAUTIONS AND INSTRRUCTIONS !!! It is basically a gun.
I dug two 8" by 4í deep holes in the ground in front of the original porch, filled with concrete and rebar, then ran a beam between them. From the joist hangers I mentioned earlier, I ran joists over the beam. Since my top step was only Ĺ inch from the bottom of the door, I left it exposed and started the pt 5/4x6 decking at the stepís edges. Once the decking was done, I added a set of pt lumber steps, a roof, and railing. It turned out very solid.
In your case you have 3", so you could cover the entire concrete porch with wood. You could simply power-nail the decking right over the concrete porch, but the one drawback of the nailer is that it is rather permanent, so that if, for any reason, you want to remove the wood at a later time, it will be messy. If possible, it would be better to attach strips of pt wood via the nailer to the top of the old porch, spaced as if they were joists, them use this wood as a base to screw or nail the actual decking to. For example, if you used 5/4 decking material for both the simulated joists and the decking, it would only eat up 2" of your available 3". I think you mentioned that you wanted to cover it with a roof, and if so loosing 2" shouldnít hurt: Having the decking raised off the concrete would allow for good drainage, and you could easily rinse under the boards with a hose so debris would not build up. Just make sure that you donít frame it in such a way that water gets trapped. Even pt has itís limitations.
First, I would decide whether I wanted to cover the existing porch or simply add to itís sides, Then, I would take string and lay out what I wanted to do for the final product. Finally, determine if I needed foundation piers dug, then build a frame just like a regular deck. It is easier than it sounds, but remember to contact your municipality for more advice and obtaining the proper permits. I have found that they can be a great source for learning how to do it the right way.
.Hope this helps. Let me know how it goes, or if you have any more questions.