Well you are a first time cruiser without the cruise experience much people has here:
Don't recomend it,
here are a few things you have to consider:
Sometimes the outside excursions are cheaper, I'll give you that,
but since you don't really know much about the islands or cruising I recomend, for now, to buy from the company.
I have read over the years a few horror stories about outside excursions,
*The ship leaving port without the cruisers, since you don't book from the company they don't have to wait for you.
*Getting rip for the money you pay, even using the company excursions it can happen...but at least you have the company backup.
I have been on 4 cruises before and I still book a few excrusions from the company that will depends on the island we will be at, mostly because I have already visit much of the islands and I know how local life is or where not to go...You have to be a little carefull depending on the island.
I live on the caribbean and from experience I know that dealing with the locals can be tricky sometimes
So enjoy your cruise and remember that sometimes paying a little extra $$$ is a wiser decision