Our kids don't even have cell phones. But they both have ipods. IF your child had an ipod, what kinds of limits would you place on their usage? Whatever it is, that is what I would put as the limit on the gaming for the iphones. That is really all it is. An ipod that also makes calls/texts.
I would also caution you (if you aren't aware of it already) to turn off "in app purchases" or your kids can run up a huge bill on itunes playing their games. And I am curious about "unlimited" shared data. I didn't think verizon offered that anymore. Or maybe that isn't how you intended that to read (maybe you only meant that the minutes/texts are unlimited). In any case, if you don't have unlimited data, your kids need to be aware of how to use their phone to stream data only when using wi-fi. If they stream movies or stream live gaming stuff, they can run up a lot of data usage quick. And you need to show them how to see how much they have used. It is really simple to do.
ETA:
As far as limits/rules? We don't have any hard and fast rules, really. We try to teach them to use common sense/common courtesy. And husband and I have final say regardless.
They are not allowed to have any electronics at the dinner table. If we are in a restaurant, it isn't a big deal, unless we are just sitting having conversation--then it would be rude, so they are put away. But if we are dining with another adult couple and lingering and the conversation has drifted into territory where the kids are not involved in it at all, then it is ok for them to have them out to play games (but no earbuds), as long as they stop if they are spoken to.
At home, we don't have any time limits imposed as far as x number of hours per day. They are theirs and they have them as they want. So long as their grades are not suffering at school because of too much digital time, their homework is done, and as long as they still do other things. They go outside and play. They take their fishing poles to the creek at the back of our neighborhood and fish. They ride bikes/scooters/skateboards. They hang out with friends outside. Sometimes hanging out means all 3 or 4 or 5 of them have their devices and play Minecraft together. Usually, they play basketball, or wander around in the woods/neighborhood, climb trees, fish, skateboard/ripstick, etc. They like being outside.
On Sunday, no electronics until daylight is gone. That means, not at church, not in the car, not sitting around the house. Until dark.
Our kids have a lot of electronics, but they are not attached to them like some kids I have seen. They self-regulate themselves pretty well. At this moment, they are playing together on the PS3. I stuck my head in to ask my son when they were taking a break next (he said he set the timer for that game for 15 minutes), and asked them to go take the dog out to play for a while. He was fine with that--no complaining.
I do not take their ipods at night. They charge them on their radio/docks and listen to music to fall asleep to while they charge.
They do know that if they misuse them, they will lose them. At our discretion. Son takes his to school (listens to it on the 40 minute bus ride) and uses it to take notes in some of his classes sometimes or note what his homework assignments are, or a web page that the teacher suggests as a help tool. Daughter doesn't take hers (though we didn't tell her she couldn't). Son is in 9th grade, daughter is middle school.
They have the same "night time" limits as they do with a standard telephone during the week. No texting/face-timing/skyping after 9:00 pm, except on the weekend. Then 11 pm is cutoff time for daughter. Son can have until midnight.
My daughter took a friend with her to a lock-in this weekend. Her friend (unbeknownst to me) brought a tablet with her. She sat and played on her tablet instead of with the group of kids. How sad for her. I was a bit irritated when I heard this (from my son, who also was there), but not surprised. She is one of those kids that her mom makes her the complete center of the universe, and so everything in her daily home life (at least what I have seen the past 3 years) revolves around her and what she likes/wants and makes her happy. She seems unaware that it is ok to not be entertained constantly. That electronics are not necessary everywhere you go. Oh well... she's not my kid.
At our house the kids have laptops, DS lites, ipod touches, Wii, and PS3. Their favorite game is Settlers of Catan-- a board game--not a digital thing. Their next favorites are CatchPhrase, Scattegories and Farkle.
Sure some days I tell my 14 year old, "Hey, you've been on that since you got home--put it up and do something else." Just like when WE were kids and our parents said that about the TV. But it isn't every day or all the time. When it is rainy/cold, he is on it more. Just like I curl up with a book more during those times.