I would always, always, be very sceptical of any offer of "unlimited" anything.
Offering you the bandwidth and disk space (as well as the management, configuration, and maintenance of the required systems) you want will
cost money. A cost that will
rise the more bandwidth and disk space you need. Quite apart from the fact that on the entire planet there is not an unlimited amount of storage space available (and so the claim is quite impossible), there will come a point where the price they offer is impractical, unprofitable, and unsustainable.
If I were you I would read the fine print very
By "unlimited" what they actually mean is "more than we think you'll ever want" and so by taking the offer you are gambling that they think people are at least as greedy as they actually are and/or they have enough overhead built in to cover for the particularly greedy. If they are wrong and/or have scrimped on the overhead, you may find the service fails to offer what it claims to.