You aren't required to run the base set adventures. If you want the skill feats, you have to run the adventure path in order (which doesn't include the base adventure aka Perils of the Lost Coast).
I run Perils though. I want to replay everything, and I want that skill feat from Perils. If you just want to "try out" a character though, just run any scenario you want. Testing characters (or even particular boons) can be fun. Then if you like them, restart their deck and choose either Perils or Burnt Offerings to play in.
I believe that the intent is for you to play the base set first. I have always done so with my groups. Here is why I think that is the best way to go:
1) You get to learn your character. Chances are, if you are starting a new character, you will want this relatively low risk starting experience. You can feel out your character and decide how you want to shape it.
2) You get scenario rewards and boons from locations. This is huge. Adventure 1 would be difficult without acquiring some much needed boon upgrades. This helps you shape your character even more.
3) You learn your team composition. Unless you are playing solo, you will want to figure out how your group will play together. Different compositions will play very differently together. Once again, this is rather low risk, so you can take some time to learn.
4) Paizo is expanding the base set adventure for S&S. This tells me that the people at Paizo want you to start in the base set and move on from there. They are expanding it so that newer players have more low risk learning, so that when they set out on their adventures, they are prepared.
Just my thoughts.
I believe that the intent is for you to play the base set first. I have always done so with my groups. Here is why I think that is the best way to go:
1) You get to learn your character. Chances are, if you are starting a new character, you will want this relatively low risk starting experience. You can feel out your character and decide how you want to shape it.
2) You get scenario rewards and boons from locations. This is huge. Adventure 1 would be difficult without acquiring some much needed boon upgrades. This helps you shape your character even more.
3) You learn your team composition. Unless you are playing solo, you will want to figure out how your group will play together. Different compositions will play very differently together. Once again, this is rather low risk, so you can take some time to learn.
4) Paizo is expanding the base set adventure for S&S. This tells me that the people at Paizo want you to start in the base set and move on from there. They are expanding it so that newer players have more low risk learning, so that when they set out on their adventures, they are prepared.
Just my thoughts.
I skip the Perils of the Coast. I find that time = money. Usually, I don't have much issues with the AP1. Although, I do find it a struggle a times. My group has played enough that we build our decks when we start with new characters. You learn what works best for the character and your play style and build off of it.
The only recommendation that I would change for the game is Potion of Healing. I think it should be a basic item that should be discarded. I just find that in most games every character should have a option to heal a little. Anyone who has played Pathfinder knows that you always have a bottle in the backpack in case of emergency.
Errata to Potion of Healing:
Basic
Discard instead of Banish.
Extra: I hope someone from the game creators sees this post and adds it in as a Errata.
I think that doing that to Potion of Healing would weaken Kyra, Cure and Drunken Master Sajan. And also, thematically, you drink the potion and it is gone. So there is no more to drink. It is a delicate balance.
Just my opinon though.
As Hawkmoon alludes to, consumables banish on use. (This includes all potions, as well alchemy objects like Blast Stones). The same is true of spells: if you don't have the required skill (Arcane or Divine), you need to banish the spell after use. In this case, think of casting the spell from a scroll instead of from memory: once you've cast it, it's gone forever.
That said, even if you don't have a Divine character, you can find ways to cure characters in emergencies.
1) Father Zantus is a strong ally in the early game, if you are lucky enough to find him. This is where the Lost Coast adventures are worthwhile; there are a lot of B and C deck boons that are quite good throughout the game.
2) Once you get your first Card feat, you can have some non-spellcasters (such as Mirasel) take a spell Card feat. Assuming you didn't acquire any spells while playing the scenario, you can pick up Cure afterwards, since it is Basic. So long as you don't acquire any spells (or banish all that you do acquire), you can keep grabbing that Cure spell back at the end of each scenario. (Scrolls of Cure are apparently easier to come by than Potions of Healing)
3) Eventually, you'll find a Staff of Minor Healing, and everything will be awesome.