You can pretty much get to around level 10 with a few hours of dedicated play spread over a couple of days.
The game gives you some dobloons (the premium currency in the game). We decided to utilise these to create extra slots in the weaponry and the rec center so we could keep churning out crafted items even when we were not playing the game.
A good thing to focus on is generating party points, the best way we have found in these initial levels is to create diversions for the minions. So basically this means adding a volleyball court, football pitch, hammock etc... And tasking spare minions on these items.
There will be some left over so you can still go collect the basic items that you need throughout the game.
However, don't create too many diversion buildings as you may not have enough left over to create the 'make stuff' items'. A Razor Clam Bed for example is pretty much essential early in the game to help you create the items you need to fulfil party supply requests. Ice moujntain is another, but can wait until you are level 10, same with red hot chili plant.
If you find that your 'make it' buildings are far apart then don't forget that you can easily scroll through and check the status of each one by selecting one of the make it buildings (eg Coconut Grove) and then hitting one of the brown left or right arrows in the popup box and that will take you to another make it building.
Same goes for the diversions, select one then scroll through the rest to make sure they are still grinding away.
Another pretty handy grind is the Fishing Frenzy mini game, you can gain quite a lot of sand dollars and even dobloons, but it does take a lot of grinding to do.
If you have any problems or questions about the initial levels of the games, just leave a comment below and we'll try to help.