Confused with Service/3G of my iphone?

So a day or so ago my phone was having troubles finding Wi-Fi so I turned it on and off of airplane mode, it found the Wi-Fi, but soon after my service depleted… I turned my phone on and off but the service did not return, I then reset the network settings and I had service again! But only due to 3G which my plan doesn't cover so it had to be turned off. I still have no service and I can't figure out how to fix it. So if you could tell me how that would be lovely?! One more thing. Does 3G cost money, if it's not in your plan, but you are connected to Wi-Fi? With 3G my phone gets 3 bars but without it goes to one bar immediately and then says "searching /no service " soon after

What iPhone is it?