Is it possible to offer unlimited bandwidth/space/transfer?

It is not possible for a web host to offer 'unlimited' bandwidth or diskspace. Such hosting plans always come with clauses that restrict how much bandwidth you can transfer at a given moment, how much CPU usage you can use (which is arbitrarily decided), and so forth

We set ample limits to our web hosting plans which the majority of website will not reach. And if they do - we're able to accommodate them with an upgrade.