When choosing a carport that is attached to your house you might want to consider a lean to carport which is sometimes called a single slope carport. These types of carports allow for proper rain run off and can allow ice and snow to melt evenly without causing pools of water that are often found on flat top carports.
If the only practical location for your carport is adjacent to your house or another existing structure such as a garage or storage building then you might find yourself limited in the type of carport you can build. Carports that fit properly in a limited space generally can only be a lean to carport which is also called a single slope carport or a flat roof carport.
Any carport with either a shed roof or a gable roof might not work for three reasons. The first reason is available space. Both shed roof carports and gable roof carports need slightly more space than a single slope carport. In order for the roof to be at a proper angle for water run off and to look proportional to the height of the walls there needs to be at least a certain amount of space. Any less space than a certain minimum amount of space just won't work. Think of at least 15 feet minimum for these types of structures. You simply can't cruch certain carports into small spaces. The second reason is aesthetic. The flow of the roof lines might look awkward with a gable roof or a shed roof. The delineation between house and carport would be clearly marked and it might look like the carport is not an integral part of the home. You want your home and carport to look as though they flow together naturally. I promise that a carport that looks stuck to the side of your house as an afterthought will not bring any satisfaction. The third reason pertains to functionality of the roof. If you live in an area that has a great deal of annual snow fall you will want to make sure that the snow won't accumulate in the seam between your house and the carport. In the spring time, when the snow and ice are melting, the runoff water needs a clear path to escape to the ground. The last thing you would want is for the water from the melted snow and ice to puddle against your home. Exposing your brick work to standing water is a very bad and expensive idea.
Lean to carports or single slope car carports tend to look more integral to the home than a flat roof carport. The same roofing material can be used and the pitch of the roof can be matched exactly. Matching the pitch of the roofs is very important. If the roof lines march then the two roofs look like they are meant to be together. Evenly a slightly different pitch can look awkward and take away from the appearance of your home. If you are considering adding a carport that has a roof at a different pitch or angle than the roof on your home do yourself a favor. Take a picture of your current home and print off two copies of it. Draw a carport addition with the same pitch roof and then draw a carport addition with a different pitch. Can you see the difference? Make sure you know what you are getting before starting the carport construction.
Flat roof carports have one advantage over the other types of carports. The roof of a flat roof carport can be used as a deck or a screened in porch. For some people a flat roof carport provides an immeasurable advantage over any other type of carport. Using the roof as a deck, or a screened in porch, or even the base for a second story addition is made even easier if there is a pre-existing window that would over look the carport. Changing this window into a doorway is a fairly inexpensive and easy proposition. An experienced contractor could probably do the job in one day but you would need to have the new door etc picked out and purchased before hand. In order to support a deck or any type of second story the supporting posts in the carport would need to be able to carry more load. There are specific formulas for determining load and an experienced contractor would be able to help you.
You don't need to make the roof into a deck right away or build a door to allow access to the deck right away. However, if you think you might consider utilizing the top of the flat roof then you need to calculate the potential load and build the supporting posts accordingly.
In conclusion, think seriously about what type of carport roof is suitable for your location, suitable for the existing house, and suitable for your purposes. It may be that you will be best served with a lean to carport or a single slope carport.
