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My favorite primer for wood doors is Bins Bullseye, pigmented shellac. This primer bonds well, hides wood grain well and gives a very smooth surface for top coats. If you prefer to stay with a latex product, then Kilz premium is good too.

Remember prep is of the utmost importance for a good finish. Sand everything and clean it well before applying primer. On a new piece, I like to lightly sand the first coat of primer. You will feel the difference, trust me. I like to use two coats of primer, then sand it again very lightly to make it super smooth: 220 grit used lightly is fine. Clean it well with a tact cloth or very slightly water dampened rag.

Now for the top coat. Use a premium quality 100% acrylic exterior trim paint. Usually a gloss or semi gloss looks great, but that's a personal preference. Don't skimp on the brush: get a good Purdy Glide, poly/nylon 2½" angled, soft chisel tip. Apply nice smooth, thin coats, and expect to do three coats for a good solid fill. Start in the panels and work your way out to the rails and stiles. If you can take the time to remove the door after it is installed, (never remove door from frame before installation!!!!) lay it flat to paint. Laying it flat will really help avoid drips and runs. Pay special attention to the panel corners and details for drips and puddles a few minutes after you apply the paint. Use long smooth strokes to finish each panel, rail and stile.

BTW, a really good latex 100% acrylic is every bit as durable as an oil based product. Oil based paints are going away and have been compromised greatly in recent years due to VOC laws. I stopped using oil paint several years ago. The only oil based product I use now is urethane.

We just use good ol' bondo to fill missing pieces in wood. In the cabinets I did last weekend, several of the doors had an inch worth of corner rebuilt from bondo.

The other tool that helped us that weekend was a profile detail sander; specifically the octosander by Skil.

You can use the same spray gun you would use for cars, but you might need a larger diameter tip/needle combo. With my gun, I need a 1.7mm tip for oil based enamel and a 2.5 for water based.

Edit to add our process:

• sand with an orbital sander and profile sander using 60 to 120 grit until the surface no longer has brush marks. It's OK if some of the original paint is still present. This ended up exposing some raw wood. Don't be afraid to press down hard on the sander at this point -- you're going for removal, not smoothness.
• Clean areas that require patching or bondo using a stiff wire brush to remove any rotten or loose wood. Mix and apply bondo, keeping in mind that the set time of bondo is typically very small and that you want to apply it in it's most liquid state for it to bond well with the wood. Do not let it partially harden as you're applying it; stop and mix a new batch. Sand bondo after 45 minutes of hardening using a wood block with sandpaper wrapped around it so that you get a surface that is smooth with the rest of the door.
• Wipe down to remove sawdust and paint debris, wait for it to dry. Apply a thick coat of primer across the entire surface. Wait for it to cure (12 hours).
• Sand any areas that show as high LIGHTLY with 120 grit. This will probably include the bondoed area and any area around where raw wood was exposed. Sand more heavily with 120 grit in areas where the primer was attempting to fill in a crack.
• Wipe down, wait to dry, Prime again, lighter this time.
• Sand lightly with 220 grit until the surface is as smooth as a baby's bottom. You want to make sure you remove any signs of any orange peel or other imperfections in the primer coat, because they will show right through to the finish coat.
• Apply finish coat smoothly and evenly. If you're in a climate like mine (hot and humid), move the door indoors to cure for > 24 hours before attempting to mount and close it.

Dad has always used exterior-grade Alkyd (Oil) based finishes on wood doors. Due to VOC restrictions, many of the finishes he used are no longer available, and the newer low-VOC formulations are prone to chalking. Our paint store, who I trust implicitly, now recommends that we use an alkyd primer and then coat with an exterior acrylic.