No. iPads that can use service plans cost $130 more. However, if you do not have a WiFi connection in your house, you will need to buy the 3G iPad or buy a wireless online router to use your iPad.
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If you have access to wireless internet connection, you can still utilize all of the same apps that you would be able to use if you bought a data plan. If you plan to use your data plan to access emails and the internet away from a stable WiFi connection, I would recommend to go ahead and purchase the data plan. If you don't like it or realize you don't use the data plan to make it worth your money, you can always cancel.
You can access internet and all data from just the standard Wi-Fi network if you have a wireless router at home. If you wanted to extend that network to get all around service with 3G or 4G, then you need to set up a monthly data plan with your local service provider.
Instagram can connect via wifi or 3G. If you have wifi, then you don't need a data plan.