We just finished our 13th this spring. We have used Cruises Only for our first couple of cruises, before the popularity of the internet. The only advantage you might get dealing with a travel agent is an on board credit or a beverage package. One thing you should know is that after you book and you see a drop in fare, you can contact the cruise line an get a reduction in fare or an on board credit.
Our sweet spot is between $150 to $200 per person per day. This can go pretty far depending on when you can go and how far in advance you can book. Your problem is going to be the number of people. With 5 you'll be looking at a junior suite or better if not two cabins.
The extras to budget for is port taxes (it will be included in your fare when you book), on board purchases (soft drinks, specialty coffees, alcohol, pictures, specialty restaurants, etc.), gratuities (runs from $13 to $15 per person per day), travel to the port and back, pre-cruise accommodations (recommended). Another expense I would recommend is travel insurance (only for the medical evact).
The cheap time is the fall. In the Caribbean, it is the rainy and stormy time. I've cruised several times and have missed a port due to a tropical storm. The most expensive time is summer and Christmas. I done three Christmas cruises and love everything except for the double the fares. I personally go in the spring and would recommend that time of year.
When thinking of a cruise, you have to consider the travel to and from the port. A pre-cruise nights accommodation is cheap insurance to ensure that you make it to your debarkation port on time. This also gives you the opportunity to take less expensive flights since you aren't tied to a certain arrival time. Regardless, you must be at the ship 60 minutes prior to sailing if you pre-check in or 90 minutes if not.
As mentioned, I would spend some time on the Cruise Critic board and look at some reviews. With the size of your party, you will be limited to two cabins or a junior suite or better. Cruising is a great vacation, we hope you have great weather and a great time.