I play a lot of pvp games on Minecraft Bedrock. I play on a Mouse and Keyboard and I don't know what key to press to quickly grab and equip things from a chest.
Not only can you shift+click one stack of items, but you can shift and double-click to obtain all the stacks of that same item.
Edit: I didn't realize you also asked to equip things. If you have any armor in your chest, you can shift+click to get it into your inventory, then right click (if it is in your hotbar) and you will equip the armor if you are currently not wearing any.
Completely unrelated, but I'll answer anyway.
For these devices:
PC (Window 10)
Just like Java Edition, you can Shift click on the hovered item to get the entire thing, or just like what @Norman Contreras said, you can also double Shift click to get all of the same items in part of the hovered item.
In Mobile, there are 2 ways to accomplish this, depending on the UI Profile setting you are using:
You can basically tap and hold the item to get the whole stack in the hovered area, but is not as quick, so it is better to use the one from Classic.
Very simple, tap on the item and it will select the entire stack in that hovered area, and tap anywhere in your inventory slot to put the whole thing in there. Faster to manage.
This bit is up to you, I don't know any controls on controllers.