What primer and paint should I used for a solid-core wooden front door?
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 2&half;" 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.