Porches, whether they are screened in or simply covered, can be built on decks or patios. When you are planning to have a porch built on a patio, there are various things that should be taken into consideration prior to having it built.
First, what roof line will work when you look at the possible obstructions from existing windows, vents, pipes, lights, speakers, etc? What roof shape is appropriate to match the existing architecture? You may have a gable, a hip, a shed, or even a gazebo shaped roof that works best with your home.
Secondly, what is the existing flooring? Is it concrete, pavers, or brick? What will you need to do to dig your footings to support the new porch cover (roof)? Is the current patio the appropriate size or will you need to expand the footprint to fit the new porch? Will the additional materials be able to match the existing materials?
Thirdly, what about drainage? Will the new porch cover have gutters? Where will the downspouts be installed? What is the grade of your property and will the placement of the downspouts work will or does there need to be trenching done to route the downspouts where you want the water to run?
All of the above items will impact the cost of your project. Different roof lines have different costs associated with them. For example, a gable roof is more costly than a shed roof generally speaking and a gazebo roof is even more costly. If you want to expand the current patio to fit a large roof, this will incur cost above and beyond the porch cover itself. You are probably going to want a ceiling fan and lighting installed so you should budget for these additional electrical expenses.