First suggestion would be to use a TA. They can get you good deals on most cruise lines, and probably give you some extra something or others. In that respect it's a little different than booking, well, any other travel. You may still want to book your flights (if needed) on your own.
What should I be thinking about when deciding on itinerary and pricing? What advice would you give a first time cruiser? Are there "hidden" costs we should be aware of or watching for?
For me, itinerary isn't as important in the Caribbean as it might be on the Mediterranean. Not to disparage the history of the Caribbean ports of call, but for my family (and more specifically, my kids), it's about the beach and one could consider them interchangeable. The Mediterranean ports obviously have that rich old world history, so if there's a specific place you want to see, find a cruise that goes there.
Also, Mediterranean cruises have a lot of port days, so a megaship like Oasis might sound like a good idea, but my suspicion is that you won't be able to take as much advantage of their facilities as you might like. Conversely, it's roughly 50/50 on port/sea days in the Caribbean, so you would be able to enjoy a larger ship like Harmony or Carnival Vista.
A final thing about itinerary - the shorter (3/4 day) cruises tend to be more of a "booze cruise". In the
DCL forum one poster noted that their Norwegian Cruise had a bunch of drunk folk on the first night, then it settled down afterwards. I've no issue with people drinking, and in my younger days I was known to have drank somewhat past excess on occasion (cough), but if that were my first cruise, and I had drunks all around me, I'd probably swear off of cruising for life. 7 days may seem like a long cruise, but I think it's the better option.
I'm not sure about hidden costs. There are, of course, extra costs and "upsells", but they're certainly not hidden within the cost of the cruise. You should be aware that gratuities are not included in your cruise price, will cost somewhere around $14/day per person, and will be billed to your room unless you ask them to stop it. I usually leave it as is, and tip extra as warranted.
Food-wise, there should be more than enough to handle whatever eating limitations you might have, whatever cruise line you might end up taking. The buffet is usually a good option in this case, as you can get what you like, and try something different as well. For dinners, the main dining room (MDR) has some daily offerings as well as standards, so again there should be no issue finding something you like. If not, ask!
I'm also wondering how important the balcony room is. Should we do it if we can afford it? Since we have no cruised before, we're not sure what to expect regarding motion sickness.
This is an interesting one. I think everyone should try a balcony room at least once. But that said, my first two cruises were outside with portholes, and the rooms were fine on the second one (the first one was in 1987-88 and I almost never speak of it) so I guess I recommend a balcony, but it's not a necessity.
If you're concerned with motion sickness, I would make sure you get some pills or those wristband thingies just in case. On the megaships it's usually smooth enough that you probably won't notice you're on the water, but better safe than sorry I say.