Both rolling and spray painting provide attractive, even finishes on your door. If you want the door to look just like it came from a factory, however, spray is your only option. Sprayed paint, when applied properly, creates a perfectly smooth, flat and even coat, whereas even the most carefully applied roller finish will leave a slightly rippled or bumpy finish. This won't really be visible from the street, however, so it will only be seen by you and by visitors, and you may even find the light texture appealing. Of course, neither method will look attractive if applied poorly -- a roller can be uneven, lumpy or streaky, while spray can leave unattractive drips.
Spraying paint requires a paint sprayer, and there are several kinds of sprayers. They pose some risks, and you must learn how to fill, operate and clean a sprayer before starting your work; improper cleaning can ruin a sprayer. This takes time, and you'll need to buy or rent a sprayer. As far as application goes, you'll most likely find the roller to be the easier choice. Rolling paint is safe, requires little setup and is fairly inexpensive in terms of equipment. As an added bonus, you'll most likely have some experience with rolling paint.
Regardless of the method you choose, you must start by removing or masking off the hardware, like the handle and lock. Clean the door and make any necessary repairs, as well, such as removing rust or filling in dents. In most cases, you should prime the door, and you can use the same method for priming that you use for painting. It's best, with either method, to remove the door from the hinges and lay it horizontally on a pair of sawhorses. It's particularly important to do this with the spray method, however, since it's difficult to control where the paint will go, and the spray will get on things other than the door. If you can't remove the door, use the rolling method of painting, since it gives you a lot of control.
With most doors, the door is not perfectly flat and has decorative ridges or recessed areas that need to be painted. If you roll paint on the door, you'll need to brush the paint in the recessed areas first, then use the roller to coat the rest of the door, starting with the inner panels between the recessed areas and moving on to the outside. If you use a high-quality paint, the difference between the brushed and rolled areas won't show. If you use the sprayer, you'll need to spray the recessed areas first, then spray the rest of the door. This can be challenging, since getting too much paint in these areas will result in drips. It's difficult to control the spray, so you'll need to mask any windows in the door or anything you don't want painted. The edges of the door area are also prone to drips.
You can use both oils and acrylics with a sprayer. Oils dry more slowly than latex paints, so uneven spots can smooth out or level. A fast-drying latex paint, however, will allow you to put the door back on more quickly, and you can use products that will slow the drying time of latex and make it spray on more evenly. Thin the paint before spraying; oils require paint thinner, while latex paints need water. There are also two basic types of sprayers: airless and HVLP sprayers; both provide a smooth and clean finish. HVLP, or high volume low pressure, is typically better for oil-based paints, and airless is often better for latex.
Rolling paint doesn't provide the same smooth coating as spraying, but using the right equipment will greatly improve the effect. If you use oil paint, again, this will dry more slowly and reduce the look of roller marks, but latex also works perfectly well. If you use oil, choose a roller with a mohair nap. Use synthetic for latex. Always use a short-nap roller. Either type of paint can be thinned to flow better, and as you paint, always make sure that the roller is full. Don't roll too much in the same spot.