Hello guys and gals! I'm here today to give you advice based on my experience and research:
Surviving Harsh Conditions in Your New World
NOTE: If you do not have time skip to the bottom

1. Resources And Crafting (very important to survive)
 - get wood (minimum 4)
 - craft workbench
 - craft wooden pickaxe
 - get cobblestone (minimum 5)
 - craft stone sword and pickaxe
 - break the wooden pickaxe by mining

If there are sheeps nearby, craft a bed. Immediately.

2. Hunger (also important if you are on Hard)
The following actions will make you lose one point: (* = not accurate)
 - walk/sneak 400 m
 - swim 267* m
 - break 160 blocks
 - sprint 40 m
 - jump 20 times
 - attack 14* times
 - get damaged 14* times
 - sprint-jump 5 times
 - regen 1* health

One of the abundant food is rotten flesh. (Warning! Calculations may be wrong.)
Zombies have 20 health points while your stone sword deal 3 damage. You will need to hit 7 times to kill one.
Therefore you can kill around 30 zombies. You can get an average of 30 rotten flesh.
One rotten flesh gives 4 points but the hunger effect for 30 seconds will take away 3 points.
7 rotten flesh can fill your hunger bar if it is empty.

3. Hostile Mobs (avoid them to survive)
Hostile mobs can spawn anytime during the night as they have 20 spawn cycles per second.
They can spawn in a pack of the same type or individually.
Mobs will not spawn within the 16m radius around you.
Even if regional difficulty will kick in and increases the chance for mobs to have stronger armor, you don't have to worry as you'll need to stay at one place for at least 10 hours for it to become significant.
Unfortunately, a new world usually starts with a full moon, which will increase chances of hostile mobs having buffs. More slimes will also appear.
If you have a bed, sleep once the sun is on the horizon, when it's counted as 'night' but light levels are not low enough for hostile mobs to spawn.

4. Summary
 - try not to sprint
 - avoid hostile mobs if you can
 - craft a sword before night
 - try to get a bed
 - sleep once you can, before mobs spawn
 - if you are planning to eat rotten flesh, don't eat them one by one to minimize the hunger effect.