The CEA2006 specs should be the most accurate. The other specs are mostly there for "Marketing" purposes to make it seem more impressive. Confusing, I know. A new head unit won't put out significantly more power, maybe a few watts if you're lucky but I wouldn't change just for that if you're otherwise happy with it.
You don't "need" an amp unless you have the top off, or want better sound quality, or louder for whatever reason. Most people are fine with just the head unit power. I'm not one of those people. Amp preferences are like speaker preferences and will differ depending on taste, budget, size constraints, etc. I would recommend that you go with a brand that is familiar and reputable. Crutchfield is a good place to start looking.
Make sure your head unit has pre amp outputs. It's not an impossible fix if it doesn't, it's just more work and parts, and you may sacrifice a little in sound quality to convert the existing speaker outputs.
I've been happy with the PPI Ion amps:
iON | Precision Power
...which aren't available at Crutchfield but I like them because they tend to be small, efficient, cheap and reliable. But there are other brands that are good too. Again it's more of a personal preference, but well built amps tend to have less sound differences than different speakers.