Minecraft wiki entry for Hardcore_mode, associated text: Mushroom fields biomes are very safe places to settle because hostile mobs do not spawn under normal conditions.
A shelter built over an ocean away from land can also be very safe from hostile mobs, unless you are near an ocean monument. However, drowned can spawn in oceans, making them not as safe. It is recommended to build your shelter a few blocks above the ocean, just in case of drowned, or ocean monuments.
It's best to build shelters out of blast-resistant materials, especially in the Nether. Cobblestone is cheap, although, if possible, permanent shelters should use obsidian.
Make your shelter as visible as possible. Proper lighting outside the shelter adds visibility, and stops hostile mobs from spawning nearby. Additionally, a large tower can help visibilty from a distance (but make sure you can get down safely!)
Zombies can break wooden doors; however, iron doors require six ingots to craft, and need redstone power. To solve this, use a fence gate with a pressure plate inside the shelter so it automatically closes. One gate will not stop skeletons from shooting over it, so a second gate can be placed on top of the first. Additionally, you can place the door such that its "open" state blocks entry, thus preventing zombies from doing any damage.
Because the shady canopies of trees will protect skeletons and zombies from burning, build an indoor tree farm to safely harvest logs and apples when necessary. For the same reason, it is a good idea to cut down trees within 24 blocks of your shelter and fully light the resulting field.
Even small farms with wheat, potato, chickens, and cows can be a great asset. Use the wheat and seeds to breed the animals for meat and other drops. Indoor farms are safer. Pigs are nice to have because pork chops can be safely eaten raw if you're caught by surprise.
Keep in mind the coordinates of your base, assuming you can obtain them.
Building a wall around your base can be extremely beneficial.