The tapping noise in the valve train is a result of the oil bleeding out of the hydraulic "self adjusting" lifters overnight. The lifters are essentially a piston inside of a sleeve and they wear over a period of miles. As they wear the tapping will get louder but will go away after the oil has worked its way into them to quiet them down. As long as they stop within a minute or two there is nothing to fear. Continual tapping means that the "piston" is stuck and this will eventually cause excessive wear and tear on your pushrod as it slaps against the valve tappet, and the valve that is being controlled may not open fully, although you would not likely feel the difference.
When I switched from dino to synthetic oil my '03 3.5l started tapping a bit in the morning, but within a minute it goes away and that was some 100,000 miles ago. The synthetic oil is a bit thinner and doesn't gum up the way dino oil does. The trade off is, IMHO, worth it. I know that the synthetic holds up to higher temperatures better (doesn't boil off) and therefore the sludge build up is minimal. I even use it in my lawn tractor engine.

As long as it quits I wouldn't worry about it too much. I wouldn't race my engine until it was warmed up, but then again I never do. Using a thicker weight oil would help keep some of it in the lifters but the trade off is in gas mileage. I've had (older) cars where the tappets were so loud I poured "motor honey" (oil so thick it looked like syrup) and it works for a while until the oil gets diluted and thinned out.