Minecraft wiki entry for Beginner%27s_guide, associated text: Doors make a 2-high entrance that can be quickly opened or closed. Depending what wood they're made of, you may be able to see through them a little, but regardless they let light through, which can tell you when dawn comes even if they have no transparent parts.
Trapdoors are the vertical version of doors, providing a one-block entrance in a floor or ceiling. (Ladders are helpful here, see below.) They likewise let light pass through, but you may or may not be able to actually see through them.
Fences are a versatile barrier; placed in a line on the ground, they block most monsters (and animals). While they look like they're only one block high, they are in fact 1½ blocks high, which is too high to jump over. (But watch out for blocks within the couple of blocks behind them, which can let monsters climb up on those to jump onto the fence.) One drawback is that spiders can climb such fences, like other blocks. If placed in a wall (that is, surrounded by blocks on all sides including the top), fences can provide a cheap window, since you can see through them (but monsters can't). Make sure the fence is visibly joined to all blocks on each side; they do not join to doors, trapdoors or glass. You can also make similar walls out of cobblestone or other kinds of stone, but these don't provide visibility.
Fence gates are a cross between doors and fences. They are 1½ blocks high like fences, but can be opened and closed.
Ladders are a flat block which you can place against a wall to let you climb them. If you leave the bottom block (against the ground) un-laddered, you need to jump to get onto the ladder, but monsters can't climb after you. As usual, spiders can still climb the wall.
A Chest isn't really necessary at this stage, but it's a convenient way to stash items you don't want to carry around. If you get killed, anything in the chest remains there, waiting for you rather than scattered around your death site. It needs to be placed as a block, then "use" the block to open its GUI and get at the contents. If you break a chest (use your hand or an axe), everything that was inside spills out as loose items, along with the chest item itself. Two chests next to each other can combine into a "large chest", see the Chest page for full details.