Cruising and going to Disney are rather similar: You can do either one on a budget, or you can have all the extras. You can do a different vacation for more money, or you can do a different vacation for less money -- the options are so varied that it's essentially impossible for us to know whether it's a "bargain" for you or not. You'll have to do the research and make that determination for yourself.
A week IS a better bargain if you're looking at the per-night cost, BUT we chose to do a short cruise first. We didn't know whether we'd be seasick, whether we'd love it or what -- our first 4-nighter was enough to prove to us all that we LOVE cruising, so we'll probably never do another short cruise again -- but if one of us'd been miserably sick, a week would've been a long trip! One negative about short cruises: The cruise lines tend to use their nicest, best ships for their week-longs, and they use their older, more worn ships -- the ones with fewer modern niceties -- for their less expensive, shorter cruises. It makes for a tough decision.
If you want to do a budget cruise for your first experience, here are a couple tips:
Book early; in fact, if you can, book as soon as the dates come available. You'll have the best choice of cabins and if the price goes up, you're already locked in. On the other hand, if the price drops, you can call up and ask for a price match.
You're looking at one of the most expensive times of year. Personally, we like fall. The weather is PERFECT, and the prices are low, low, low. Of course, it's hurricane season, so there's some risk -- no, you won't be sailing through a hurricane (the captain has the authority to change your itinerary at the last minute if there's danger), but you might miss a port or end up visiting a different island.
An inside cabin is your cheapest option, but I personally have a "thing" about not having a window. I'd be a little freaked out by an inside cabin, so I insist upon at least a window cabin. Right now, since we cruise with two children in the same cabin, we always book a balcony. It's the cheapest way to get extra space, and though four in the cabin is do-able, that little bit extra is worthwhile.
Study the deck plans to see where your room's going to be located. If you're going to have four in a room, try to get a cabin near the gym (so someone can go there to shower when everyone's trying to get ready for dinner) or near a public restroom (because four sharing a bath can be problematic at times). If you're going to get a balcony, consider an aft balcony; they cost the same, but the balconies are MUCH bigger -- ours on Mariner of the Seas was literally half the size of our cabin (we had two loungers, two deck chairs, and a table out there, and there was space to walk around).
If you're within driving distance to a port, obviously you'll save by booking a ship from that port. It might cut down on your options, but driving is much cheaper than airfare x 4.
Regardless of whether you drive or fly, most experienced cruisers will tell you to arrive a day ahead of your ship's departure and stay in a hotel near the port. It's cheap insurance. If somehow your plane is delayed, or if you end up stuck behind an accident for hours (it happened to us!), you won't miss the boat -- literally.
If you're going to Port Canaveral, Country Inns & Suites is a great option. We paid $99 for one night, which included breakfast the next morning AND we were able to leave our car in their parking lot for the week while we cruised. It would've cost $12.50/day to park in the cruise ship's parking deck. CI&S has a shuttle that runs people to the port and back for $4.50.
Your meals will be included in your cruise ticket, BUT there may be extras you'll want: The adults-only specialty restaurants cost $20-25 per person, alcohol obviously costs extra, speciality coffee drinks and milkshakes might add to your cost. Sodas cost extra on most ships.
You'll need to pay some hefty tips on the last night of the cruise. Considering the amount of service you receive, it's not a bad price at all, but it's probably $300-400 for a family of four, so you'll want to be sure you've included it in your budget.
Do you already have passports? If not, include the cost in your budget.
When you stop at the islands, you'll want to do something special. The ship's excursions are EXPENSIVE (plus you'll be in a huge crowd, and will end up being shuttled through the shops that give them kickbacks, and you'll have to eat and use the restroom on their schedule). Instead, search the internet ahead of time for private vendors who offer a wider variety of excursions. We have been THRILLED with all the private excursions we've taken, AND the price has been considerably lower than the ship's price.
There'll be a live show every night -- perhaps dancers one night, comedians another -- and it's included in the cost of your cruise. There'll be a movie theater too. There'll be plenty of sports onboard: pools, a basketball court, ping-pong tables. Expect a library and a game room (as in Monopoly and Sorry). Expect dancing every night. For money, you can play bingo (and win big prizes) or visit the spa for masages, facials, and the like. For kids there's an arcade with outrageous prices. If you're on one of the newer ships, you may have a rock climbing wall, an ice skating or inline skating rink, putt-putt golf, and more. You won't have time to do everything that's available.
The ship will offer you LOADS of opportunities to spend money. When you get onboard they'll hit you first with the chance to buy a $40-50 all-you-can-drink soda mug. Outside the lunch buffet they'll be selling silver jewelry. On the last day they'll run a special on logo tee-shirts and jackets. They'll push their island excursions hard. Everywhere you turn, you'll be offered mixed drinks. You'll be able to buy a cookbook with the dining room's best recipes. The daily newspaper -- which will give you the times for island stops, shows, etc. -- will offer specials on this and that. You'll not be made to feel bad if you don't buy, but there is SOMETHING everywhere.