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As far as I know you are only eligible for priority boarding / check in if you are enrolled in Royal Caribbean's loyalty programme, the Crown & Anchor society.   You have to have cruised with them to earn points and you start at Gold level.  This means a separate queue at check-in which may mean you can board quicker.  There are so many people who are return cruisers the queue may be shorter for first timers!
Some cruise lines match the loyalty status - maybe your status with Carnival transfers over but I'm not aware of that.
If you're staying in a suite or are sky / star class (will depend on the ship you're on) you may qualify that way. 
What ship / what kind or room are you in?
 

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Are you in a suite?  What ship and what port?
If you've never sailed with RCI and are not staying in a suite you won't have any priority boarding.

With Royal, the Suites and high end reward members get priority boarding.....and  a separate lounge at some ports to wait for boarding. As for rooms being ready first, not in any of the regular rooms that I know of. Someone here may be able to confirm about the suites but I don't believe so, at least on any cruises  I have been on I am not aware of.

Priority embarkation can refer to one of two things: guests staying in a suite, or guests in Royal Caribbean's customer loyalty program known as Crown & Anchor Society.
With Crown and Anchor, they board guests in reverse order.  So they start with the top tier guests, and then move down through the C&A ranks before boarding non-C&A guests.

Chaotic is nothing until you have seen Disney....they board you one family at a time. It is meant to be personalized but it is so drawn out! So basically you check in at the pier and get a boarding number. Then you have to wait till they call your boarding number and as you proceed on board they call you one family at a time to welcome you. So as you set foot on the ship there's crew there and they say "Welcome _____ family!" and of course you pose for a pic. Seems like a cool idea but when there literally hundreds of people in the terminal it's long.....Royal's system is way better.

The good news is that even without priority boarding, the RCI boarding process doesn't seem to be as chaotic as Carnival.  I've sailed Carnival more times than I have RCI and before switching to RCI in 2016 I endured some absolute chaos boarding Carnival at times.  So much so they created their FTTF program to sell you a way around it.  I've never felt the need for that on RCI.    
It can vary by port as not all terminals are created equally, but RCI built the cruise terminal in Ft Lauderdale with Oasis class ships in mind and they took time to look at how to board 6,000 guests without chaos.  They are doing the same in Miami with a new terminal there and they will begin rolling out even more boarding enhancements with the mobile check in functionality of their new app coming in 2018.  
Cabins are typically ready at 1pm for all guests, suites down to inside cabins.  Sometimes though they are able to open cabin access earlier.  Star Class suites is the exception.