You can have the best smorgasboard of items, but you won't get places without the right armor and weapons. Armor is far more generalized than weapons, but if you have multiple weapons to pick from, be sure to pick the right one. Different monsters have different weak spots and elemental weaknesses. Some monsters take a ton of damage to the head, so if you know how to use a Hammer, consider bringing one! Or maybe you know you need to chop off a monster's tail, so bring a cutting weapon.
You must also consider things like elemental and status weaknesses. Duramboros, for example, can be easily afflicted with the Poison status ailment, which helps because he is a damage sponge. So consider bringing a poison-inflicting weapon. Lagombi is very weak to the fire element, and so is Lagiacrus, so if you use a weapon with lower raw damage, such as the Sword and Shield, be sure to bring a fire element weapon to give you that extra oomph.
Once you've put together multiple sets of armor, make sure you pick the right armor set that is good for the quest. Just like monsters, armor will be weak to different elements depending on the monster it was crafted from. If you're going up against a monster that lets loose a lot of fireballs, you don't want to be caught blasted with armor weak to fire! So don't wear Lagombi armor.
You got everything together? Okay, one last thing to do before you leave. Eat at the kitchen. You will receive food skills that will help you immensely, and could even boost your maximum health and stamina, letting you take more hits and dodge more!
This is just an overview. All equipment and the kitchen will be discussed more in detail in their respective sections.