I have the same engine in our '07 Chrysler Town & Country. I did try Mobil 1 5W-20 in it, once, and left it in for a few hundred miles. The engine was real noisy on that. I drained it and put some Pennzoil Conventional 5w20 in it and it was much quieter, though still not perfect. It runs excellent on Pennzoil Platinum 5W-20. I'm currently running a stash of Havoline DS 5w30 though it (mostly from my recently sold '07 Corolla). I like the Havoline for this application because it's already a thin 5w30, so in service, it's likely down into the 20 weight grade before long anyway. Plus, I can feel the engine more on 5W-20 compared with 5w30. There's a touch more "refinement" with 5w30.
This is a good engine that will last you a long time. It has a good torque curve and is quiet and smooth. It doesn't have quite the low-end bias that the old 4.0L did, but in my opinion, the 3.8L has so many other benefits that the point is rather moot. The 4.0L has a steller reputation for reliability, but I think you'll find that the 3.8L will age extremely well also. This is the second engine of this type I've had (first was the 3.3L in a 2003 Grand Caravan) and we haven't had a lick of trouble out of either engine.