Q: Can you use Battle Fury and use another card to prevent the 1 damage to my hero and still ready my hero?

A: No. You must pay the cost fully before you can trigger the effect. If the cost is to take a damage but you prevent the damage, then you have not paid the cost and therefore cannot resolve the effect. -(Developer Ruling, Hall of Heroes)

Importantly, at the time of writing, the ruling listed here has been updated and effectively overruled by FFG (which is something that happens fairly regularly, so be logical when it comes to which developer rulings you choose to follow, and don't take them as being written in stone).

Taking damage is not the same as dealing damage. So you can prevent the damage (for example, with Tough) and still be considered as having paid the cost, as the damage was dealt, it just wasn't taken. See Ruling #260 on Hall of Heroes (amongst others affected by this new ruling).

As far as actual reviews go, Battle Fury is pretty invaluable if your hero regularly has 3+ ATK available to them, and has decent defensive ability and recovery. In multiplayer, this combos heavily with decks that focus on readying, like Repurpose-focused protection decks, Quicksilver, or stat-boosters like Spectrum and Rogue, as you can hand them out to the rest of your team. So think beyond just how useful it is for your own hero to ready up!