Painting a front door can be done with several methods; brush,roller or sprayer. All of these options should be determined based off the style of the home and age or pre existing damages that the door might have. For a home that has an old tuscan look such as rich wood trim and skillfully placed stone having a done by hand look with tools that match the era of your home is best so having that door done by Brush would be best for matching the style of the home. Now if the home is modern and the door is new then a spray finish is best to maintain the slick and smooth finish that will go with a modern house. Only sometimes due to damages or mistakes made by past trades there are small imperfections that need to hidden and the best way to hide those imperfections is to use a roller this gives a look that works well with any home and covers imperfections with a new texture from the roller called a stipple. As for the finish that should be on the door is based on personal preference only most doors are painted with gloss, semi gloss or eggshell. The higher the sheen the easier it is to clean and is more resistant to fading and looks newer longer yet if the door has damages that are repaired and is not taking direct sunlight a lower sheen is a good option to help hide those imperfections.
typically the cost of refinishing a door can be as ranged from $250.00 to over $5,000.00 depending if the door is standard or custom.