many royal caribbean ships have rooms for 5-6 passengers, but they are not available online - you have to call to get pricing. sometimes (usually) they are cheaper than two rooms, sometimes getting two connecting rooms is cheaper.
the only for-sure extra cost is tips, which are $12 or $13/per person per day (they just raised them and i can't remember - i think they are $13 now). tips are charged for everyone, even babies or toddlers.
parking at most ports is between $15-20 per night. at port canaveral (near orlando) it's $20. there is off-site parking at most ports that is about half the price, but you have to take a shuttle to the port and back - for a 4-nighter with 6 people, it may or may not be worth it.
spa, excursions, and souvenirs do cost extra, but there is plenty of free stuff to do on the ship - i've had trips where my extras totalled $5 other than tips. being that it's your first cruise, assume you will want some souvenirs - there's expensive stuff, but plenty of cheap stuff, too; there's usually a t-shirt sale one day where shirts are $10, and usually the ships sell pandora charm bracelet knockoffs that are fairly inexpensive, as well as magnets, mugs, toy ships, and that sort of thing. depending on where you go, if the ship-sponsored excursions are very expensive you may be able to find your own excursions cheaper by doing some online research on tour guides etc.
alcohol, sodas, and specialty drinks (frappuccinos, virgin cocktails) are also extra. if you are soda or alcohol drinkers, royal has packages you can purchase which might make it cheaper. there are also specialty restaurants which cost more for dinner. if you plan on eating at 3 or more of those, royal has started to introduce packages for those, also. that said, the main dining room food is good, and on a four-night cruise, there's probably no need for a specialty restaurant if you're trying to watch your spending.
i book directly with royal, so don't know anything about vacations to go. i'd just do some online research, and maybe check chris elliott's website (he's a travel writer who helps people with complaints) and maybe the better business bureau (though there are bound to be at least some complaints for any big travel company). policy on the disboards is that we can't recommend travel agents, as the site is run by a
travel agency.
to get back on the ship you need your seapass cards (those are your room key cards) and a photo id for adults - we just use our licenses. passports stay locked up in the room safe for the duration of the trip. i believe kids don't need the photo id, but i'm not sure of the policy as we don't have kids.
i hope that helps!