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.
Its always best not to go with such a host that offers ''Unlimited or Un-Metered''. Most of these host are just resellers using a reseller account. ALWAYS go safe.