I've been trying to level all the remaining four classes at the same time so that I can compare and contrast them, so I have gone through the starting 5 levels 5 times now and have the following pieces of advice for anyone who is still at that stage of the game or is about to run an alt.
Firstly, don't worry about saving your companion training points at this stage in the game. Spend them all, or as many as it takes to get you companions up to one level below you. Any less that that at this stage in the game and you are bound for frustration.
Don't be worried about joining a group for combat. At this level, especially in the Skull cave, you may not be able fight anything without a group! That area is quite crowded. Doing this will give you a bit extra gold and a better chance at gear. Equip whatever the first pieces of gear you get and make sure that before you get too far in Skull cave, you check the treasure chest up on the shrine as you walk through. It will give you a class-specific piece of gear.
All of the battles in the starting area are pretty straight forward until you get to the Defeat the Troggies quest where you have to activate the three pillars. The best way to do this is to have you companions split up, sending one to the top, one to the bottom and your pirate to the one on the other side of the board. Once all three are in position, activate all three pillars on the same turn. Since each pillar adds two troggies to the board when activated, this avoids them getting in your way. You don't even really need to fight any of them, as you get the same rewards no matter what.
For the Fin Dorsal fight, just get to him as fast as you can and ignore the other sharks. If you can, hit him with Bonnie Anne's special move to reduce his dodge. That will make him much easier to hit.
Next, you go back to Skull Island and are shown your ship, at which point you start the Ratbeard quest chain and get your third companion. Make sure that, on the way to see your ship or the way to the tavern, you stop in every shop there is (clothing, weapon, ring and the totem vendor who is up on a platform) and buy every piece of gear you can that's an upgrade. Focus on dodge as it makes a huge difference at this level. If you can't find a vendor, just look it up on the map.
When you fight Ratbeard, focus on all the other rats first and ignore him. He runs away anyway, so don't waste your damage.
When you go to Blood Shoal, you pick up quests from Manny, Moe and Jack. The best way to do these is to do the quest where you talk to the crab first. This one sends you to sink cutthroat ships for 6 ropes. Make sure you hit the ship parts vendor on Blood Shoals and buy whatever equipment you are missing, prioritizing cannon, then rudder, then anchor and, if you have any cash left, upgrade the rest. When fighting the cutthroats, don't board them if you can avoid it. It's much faster to just sink them. If you accidentally get boarded, just flee. It's a short trip back from Blood Shoals and it's much faster that way than to actually fight hand-to-hand.
Once you have all 6 ropes, use the "warp to life fountain button" to go back to Blood Shoals and turn in the quest to the crab and then to the ghost rat. At that point, you will hit level 5. Spend your training points (you will get 6 of them) to get all of your companions to level 4. Get your new ability from your class trainer by warping back to Skull Island. By doing it this way, the Batacuda fights and the fight to rescue the mouse boy will be a lot easier.
That's the advice for now. Once I have taken all of my alts through the Presidio, I'll write another one of these. Hope everyone is having a great holiday weekend!