(UPDATED to include info about Mojo Potions)
This guide starts at level 5 in Jonah Town and runs all the way through the end of the Presidio. I'm focusing on the main questline up until level 10 because you don't level any faster with the sidequests than you would without them and I don't think you can get to level 10 any faster by doing them. You could grind it out, I guess, but I don't like just grinding experience and prefer the questing method, so that's what I focus on in these guides.
At level 5, you have your raft, you've finished the cave with the ghost rats and have headed to Jonah Town looking for Ratbeard, as you are both after Gunn's gold and he has the head start! When you get to Jonah town, you are first told to rescue Brody from some sharks in a nearby vortex. A lot of people have had trouble with this quest, and there is a chance you could get in trouble with it if you're unlucky, but if you get over to Brody as fast as you can, you shouldn't have any trouble. The encounter starts when you board his ship. The sharks go first (this is where you could get unlucky. If more than one of them gets a critical hit, there's nothing you could have done and Brody dies) and then you get your turn. If you're a buccaneer, you can use Mighty Strike to rush over and start mixing it up with the sharks. Any other class, just get over to his ship ASAP. The goal at this point is to give the sharks more targets to worry about than just Brody. Focus your attacks on one shark at a time and you shouldn't have any trouble. I think the worst that's happened to me on 5 runthroughs of this quest was I lost a Bonnie Anne. When you turn this in, you should be level 6.
Next, you're sent to look for another pelican on an island of Water Moles. They have you down some ships from a neighboring tribe. These aren't that much different than the cutthroat ships, though they may be slightly higher level. Just make sure your raft is equipped with anything you've gotten as a drop (or that you have bought all the best gear from the vendors on Blood Shoal and Jonah Town topside) and you shouldn't have any trouble. Make sure you give this quest a priority as it awards you your first Mojo Potion. Mojo Potions, when activated, revive all fallen companions, and return your pirate and your ship to full health. That's a lot of power at your disposal and a life saver in dungeons. Recharge the Mojo Potion by collecting blue yum you'll find floating around basically everywhere you go.
After that, you're sent to Skull Island sewers to rescue the Pelican the Water Moles told you about. There's nothing terribly difficult about this fight either. The same strategies you have been using will apply here.
Once you rescue the pelican, you head back to Jonah Town and are able to go down to Gullet to meet the Frogfather. There is a brief skirmish when the password you are given turns out to be bogus. In this fight, you can get a little advantage by causing the barrels to explode. All the enemies start out on the other side of a barrier rigged with explosives. So, if you have a ranged AoE attack (I usually use Bonnie Anne's scatter shot for this, depending on how she's positioned at the start of the skirmish), you can get a little HP off of all the enemies. After you have defeated them, talk to the Frogfather and get your 7th level.
The Frogfather sends you to the Presidio, the first instanced dungeon in the game. It's fairly straightforward but there are a few things you can do to move through it quickly and safely. One big tip is to make sure your Mojo potion is full before going to the Presidio. No matter how well you do, there is a good chance that at least one of your companions will go down at some point. Don't be shy about using your potion! You can recharge it in the court yard with all the blue yum fruit there. If there is no blue yum floating around, go inside your next area and go back outside again and some new yum will have spawned.
The first step is to try and sneak past the Monquistan guards. If you are patient and watch their patterns, you can sneak by all three sets of guards on the wall before you go down into the courtyard. I have gotten past them without incident 3 times, so I know it's possible. Just make sure there isn't one facing you and make a run for it! After you get down from the wall, there are no more skippable fights, so don't bother trying to sneak around anymore.
You fight several sets of guards, all standard strategy will apply. You are then introduced to the companion you selected through the "How did ye lose your parents" question you were asked at character creation. Once you get to them, they'll tell you to get the key to their cell to let them out. To do this, you fight the boss of Presidio. This fight has a "kill the boss" victory condition, so ignore the other Monquistans and focus on the boss. This is an Epic fight, so you get to choose which companions will join you. Unless you bought a few in the crown shop, you'll only have 3 companions anyway, so the choice is easy! If you do have to choose, make sure you bring Bonnie Anne. When the fight starts, run all the way across the board, again ignoring all the other Monquistan guards, and focus fire the boss. The reason I say to bring Bonnie as is so she can use scatter shot and reduce the boss's dodge.
Once, you have downed the boss, be sure to grab the training manual that's sparkling on the ground to the right of his desk. Then you can release your new companion, fight one more battle with the new companion's help (he won't be under your control yet) and then head back to see the Frogfather. At that point, you get level 8, the companion you just freed and the next quest is for your new ship. Stay tuned for the next guide that will take you to level 10 and the conclusion of the Ratbeard story arc.