All three netbooks have Wi-Fi built in, but only the Sony packs a Verizon 3G EVDO module, which allows you to connect at broadband speeds almost anywhere in the U.S. -- a great perk. The Sony was running Vista, though, which made it much slower than the other two machines, both of which ran Windows XP. Nevertheless, it proved to be a nice, light e-mailing and communication device.
Bottom Line: Screen resolution trumps everything else for me, so I would go for the HP Mini. The Sony VAIO P would fit well in a designer purse, which suggests that Sony might be targeting fashion-conscious women. I wouldn't be able to use it on a daily basis. If style is not your main concern and you want a versatile all-day companion, I recommend the Asus Eee PC 1000HE.