The only blocks you can break are leaves + mushrooms + vines. You can use the breaking of leaves + vines to your advantage as far as moulding a tree into some sort of fortress or a hiding spot in areas of dense foliage. You can also break leaf blocks to get apples, but they're rare.
As far as going to the chests is concerned, it's best to go to the chest nearest to you, raiding it, and then burning rubber out of there, getting far away.
Good tip as far as getting to the chests is concerned, start your double sprint a few seconds early. Sure you'll get pulled back by the 'force field' but it means you'll be sprinting to the chests as soon as you're able to.
Also:
Use shift click to place items in your hot bar faster.