I have and love the P4's on my Altima(205-65-16). Great in the foul weather, good on snow/ice. Better than one would think by just looking at the tread. They hold the road in the corners and track nice and straight on the highway. Better than one needs for normal type of driving but, they're not a HP tire, just a really good a/s tire. Highly rated on TheTireRack and Consumer Reports. The TRZ's are highly rated as well and so are the KR-21's and AltimazHP. And of course the Michelin Primacy MXV4.
The highest rated on both the tire rack and consumer reports is the Michelin HydroEdge but, they're the most expensive of all of the tires you mentioned except the MXV4's. The HydroEdge are usually T rated maybe H too and the Primacy MXV4 are H rated. Most of the other tires mentioned are either T & H reatd or just T rated.
Another tire that is highly rated and gets great customer reviews is the Hankook Optimo H727. I'm thinking of installing these on my daughters 06 Mazda3i(205-55-16). She doesn't need a performance tire as she drive in Buffalo, NY and any of the tires that you or I have mentioed in this post is more performance than she will ever use. I can't beleive how nicely all of the tires mentioned here, handle in the corners and how well they track on the highway along with being smooth and quiet. I have driven may vehicles with KR-21, P4, HydroEdge and TRZ and they too are great tires. Only drove one car with the AltimaxHP and they too were nice. If you just looking for really great all-season T or H rated tires, you couldn't have chosen a better group.
As a dad, Im very concerned for our kids. So, buy online and pick just about any of the tires mentioned. I usually visit some local tire shops and look at the tires sidewall and style to see if it will look good on my vehicles. Also check the tirerack for consumer ratings in the area that your buying tire for. Example, I want a/s tires that do well in the snow/ice but are also nice riding and handle decently. I already know that most tires do well on dry roads! Get a price installed and check online. Right now as it stands, I'm choosing the Hankook Optimo H727. I usually leave the Michelin's on the shelves. Not that they aren't great tires but, they're usually way too much money for only being a little bit better.