if I were to purchase a Refurbished iPad 2 would there be damage?

Refurbished devices are restored to the newest state as much as possible. This means it wont have any scratches or marks. It will have been repainted or repaired with new covers and screens where there had been previous damage. If you make a cellular data contract with Verizon, then yes, you would have to pay a bill each month. The price would depend on how much data you initially planned to receive or have used in total for that month.

My family in total has bought 4 macs and 3 iPads all refurbished and never had a problem (except one iMac that broke because it was dropped by the UPS guy, which apple replaced for free)

All Apple refurbished products have brand new screens, batteries and outer cases. The only parts that were ever used are the computer chips. You have nothing to worry about, plus they have a great warranty and by far the best customer service I've ever talked to. They actually offered to upgrade my iMac to a brand new 27 inch if anything went wrong with the replacement!

And you are correct, your 3G will be billed monthly through Verizon. I'm not sure what iPad-only plans are like, but I know that if you have a shared data plan with Verizon it only costs $10 a month to add an iPad.

If you get it from Apple it should look brand new. The only noticeable thing is the packaging. INstead of a fancy box it's just a white box that says iPad. As for the internet usage its optional to pay monthly. Lets say your'e going on a trip next month and you need 3G, you turn the service on within the iPad. Then when you don't need it anymore you cancel the service without paying any fees for cancelation. There's no contracts

Since its refurbished it should not have scratches on it.

You do not have to pay for 3G service if you do not want to but if you don't pay for it you can't use 3G service when you don't have wifi