Difference between BF4 and BF1 armor
Unlike in BF4, where only AT weapons dealt any damage to tanks, in BF1 most weapons deal some (albeit little) damage. Regular frag grenades, incendiary grenades etc. In fact the recent Fall Patch has increased the damage regular grenades deal to tanks.
Another thing is that unlike in BF4 where rear-armor was a tank's weak spot, in BF1 it's the tracks. Tanks can be easily immobilized if attacked from side.
AT weapons
All classes can equip light AT-grenades, which deal much less damage than heavy AT-grenades, but are lighter, and thus easier to throw farther.
Once you level up your assault, you'll gain access to AT mines, as well as the AT "rocket gun".
Snipers have K-bullets, which are specifically designed to damage armor.
Anti-tank rifles spawn as a battle-pickup (for example there is one at E flag on Sinai Desert Conquest).
Field guns and fortress guns also do high damage to armor and can be operated by any class. Their downside is that they're stationary.
HE mortar can do significant damage to tanks without the need of exposing oneself to direct fire.
AT mines, which can be dropped either by Assault or Artillery Trucks are extremely effective - 3 mines can currently take out any armor in the game.
And of course, tanks are vulnerable to bombs dropped from airplanes. The Attack Plane can be equipped specifically for tank hunting.
It seems the usual knife animation has been removed (you could move straight from a gun to knifing someone), it is not mentioned on this page for the take-downs on the battlefield wiki. Instead, a melee weapon must be equipped and used, as seen in this video.
Best Answer
During the beta, the only way to buy weapons and accessories and to edit your loadout is during a game.
While you are on the respawn screen, you can select a class loadout, then you can use your controls to move inside that loadout and select things like your main weapon, side arm, grenades, tools, etc..
Then you press the correct button * to access the sub menu, inside this menu you will find new items you can purchase with your war bonds and you can also select purchased items to spawn with.
The same way applies for vehicles, which is annoying because this means you have to wait for vehicles to be available to be able to customize your loadout.