What would happen if I put another sim in my iphone?

I have an iPhone 5 for verizon which is unlocked for all other carriers. And it is a SIM card phone. I'm going to Mexico and I was wondering of I put a mexican SIM card in my phone will I lose all my info? Or what is the situation? Also I might switch to att and if I put an AT&T SIM card in my iphone will I lose all my contacts?

How do you know it's unlocked? Even if you buy "SIM free" iPhone it is getting locked to the first SIM you put in your phone
But if your phone is truly unlocked then yeah - you can put any other carrier SIM -no problem. It will just work
You are not gonna lose any info (you might "lose" some contacts if they are saved on your Verizon SIM which is unlikely as smartphones don't save numbers on to SIMs by default)

If its unlocked just save your contacts to the sim card you need them on and you can put in any sim you want as long as the phone is unlocked