Can I buy iPhone online @ apple store then use TPG sim card?

So my brother thinks you can buy an iPhone at the apple store and then can put any sim card in it and it will work exactly the same as when you put Vodaphone, Telstra, Optus.... blablabla.. sim cards in.

Is that true? or is he full of himself?

Will the internet work the same, itunes.. apps? everything? or do you HAFTA be on iphone plans that they only offer... what are my options.... I rather buy outright and have my phone unlocked and be on TPG because they have good (no contract) plans. plans that suit me.