Welcome to the basics of hunting, which is NOT hunting at all actually.

When starting a new save of Monster Hunter, you are pretty much forced through a psuedo tutorial. Gather herbs and probably some mushrooms, it's customary to all games, but Generations eases you through the early stages. But that doesn't mean you should just ignore these quests, it's generally a good idea to get a fair amount of Green Herbs and Blue Mushrooms to combine and make potions with. Combine Honey with those potions and you get MEGA Potions that replenish your health incredibly. Having a good base of items to start your hunting is generally what the tutorial is for, if you try to tred through hunts with few potions, it will not end well for you.

Your hunter's inventory only allows for a granted amount of items inside it, generally in the 10s. 10 Potions, 10 Mega Potions, 10 Herbs, such and such. You can customize your hunter's inventory however you like, but a general inventory (in my opinion) is 10 Potions, 10 Mega Potions, 5 Cool Drinks, 5 Hot Drinks, A Farcaster, and a couple Paintballs. I will go into detail into explaining these items at a later date.