Well I love my I-phone 4S! I got it last June. Best Buy has a wonderful return plan (for about $15 a month, if it quits working, and demonstrates it's problem while there they'll replace it with the latest model).
Local weather app... Check
Reception, pretty good
Fits easily into small hands... It depends on your case. I got the heaviest Otter box I could find (it came with the phone). Being the queen of klutziness, I drop and throw (accidentally) it a lot. So far so good.
Verizon friendly... not sure, I have Sasktel.
Pictures and videos.... Check
Cost... depends on the plan you get. I got a three year plan, and the highest data I could (10 GB a month)... I pay around $90 a month. There are smaller plans out there of course.
Also ease of use, it's my first cell phone. I find it very easy to use. Love it! And if it breaks, well I'll probably get another I-phone.
My brother just got a Samsung Galaxy (the latest one not sure the number), it's a lot bigger than mine. He likes it.