With new cabinet doors and fronts, you need to make sure you get a good quality primer. I prefer the Zinsser brand of primers, but Sherwin Williams also sells a very good primer designed for raw wood. For the best results, easiest clean up and durability, nothing comes close to an oil based paint. Semi Gloss is the most common sheen used.
After sanding and cleaning with both a rag and vacuum, I would prime with the Zinsser BIN oil based primer, then after a full day of drying, I would pain with a good quality oil based paint from Sherwin Williams. The box stores just don't carry good oil based paints.
I have a Gracco HVLP spray gun that does a very nice job. The quality of the gun will show in the finished job.
Remember to tape and cover everything with plastic. When you spray, a small percentage of the paint will float in the air and settle on every single exposed surface there. Where a mask and cover every bit of skin you can, because what you miss will also have paint on it that you will have to use paint thinner to get off.
If you do not want to go with oil based and a brush/roller finish is acceptable, then stick with Valspar at Lowes or go to the specialty stores like Sherwin Williams or Kelly Moore. Paint went through government regulations a few years ago and they all had to reinvent it. Some companies that used to make decent paint, like Behr, don't anymore. Valspar is the only box store brand that is still half way decent. Also be aware that paint with primer in it is just a sales gimmick to try to make their paint sound better then paint without it. All you are getting is a better grade of paint. You cannot replace what primer does, which is bond and seal the surface to allow better adhesion of the paint with a uniform finish.
Go with a good primer. For brush or roller, I like the Zinsser 123 for raw wood and sheetrock.
With paint, you get what you pay for, and the more effort you put into it, the better the results.
I've never heard of or used a clear coat on a painted cabinet. Clear coats are for stained wood.
Eddie