Best way to use my Verizon iPhone 5 while studying abroad in London?

I was told that I can put the phone in airplane mode, turn wi-fi on (wherever I have it) and there won't be any extra charge on all apps/texting/calling.
I was also told that in addition to doing this, I can buy a SIM card in London for calling/texting in a pay-as-you-go manner.

I know very little about cell phones/data plans/SIM cards/anything technology-related, so I would like some clarification on this stuff. I know the international plan from Verizon (especially for 3-4 months) is astronomical so I'm looking for the cheapest/easiest way I can use my smartphone abroad. For the most part, I would just be texting with people back home who also have iPhones, so we would be using iMessage instead of texts (which counts as data, correct?).

I'm clearly clueless about this stuff, please help!

Why not email them? Saves you a big headache, since you are not familiar with INTERNATIONAL plans.

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