My family and I have went on several cruises (all of
Royal Caribbean). As far as vacations go, I think it's more budget friendly than most. That being said, I'd NEVER go over Easter break. The prices then are much higher than normal, and the ship will be chock-full of kids. (Don't flame me for the kids comment, but if you want a peaceful relaxing cruise it's hard to do on a ship with 1000 to 1500 kids, many of whom are unsupervised by their parents.)
We like to cruise in January (skip New Years though...the prices are high). The prices are rock-bottom in January, and hurricane season is well over. The weather is beautiful...usually in the mid-80's in the Caribbean. In January, the passengers are mostly adults, rather than kids. If you want a boat-load of kids for your own kid to play with, this might matter to you. My son is 19, so we'd rather go when there are a couple of dozen kids, compared to 1000-1500.
You asked about budget. Here are a few things off the top of my head:
Don't go over a holiday period. December (minus Christmas), and January are the cheapest months. February (minus Presidents Day week) has good prices as well. September and October are cheap too, but it's hurricane season and that's a chance I don't take.

November (minus Thanksgiving week) is a toss up...it's cheaper, but the threat of hurricanes is still looming.
Inside cabins (no window, no balcony) are the absolute cheapest. Sometimes we spring for a balcony cabin, but sometimes we go with a cheaper inside cabin. It depends on the intinerary, and how much time we expect to spend there. On a typical 7 day cruise, you'll spend very little time in your cabin. However, I've taken a couple of long cruises (14 and 16 days), that have multiple "sea days", and the extra cost of the balcony was well worth it to me.
Someone mentioned tips above. Tips are really not as high as you'd think. You tip your waiter, assistant waiter, and room steward at the end of the week. Tipping the maitre de is optional...depending on whether he has provided you with service. Overall, tips are about $11-12 a day, per person in the cabin (including children). The bartenders get an automatic 15% of your drink price...you can tip them extra if you want, but it's optional.
Pop and alcohol are not included in the cruise price. You can buy a pop card for a few bucks a day. We never have, as we don't drink a lot of pop at home anyway. Things like iced tea and lemonade are free, so we just drink those. On Royal Caribbean, juice is free at breakfast...not sure about the other cruise lines.
Shore excursions through the ship can be expensive. I'm an obsessive planner (aren't all DIS'ers?

), and I arrange our own through local companies. I save at least 1/2 by doing it that way, and instead of being with a huge crowd of people on an excursion, ours are much more personalized...sometimes just my family, sometimes with just a few other people.
I do a lot of research on cruisecritic.com. There are sections of the board for each individual cruise line. There are also sections for the individual ports of call. I research our shore excursions on the latter, since there are often recommendations for individual tour operators.
I'd really think about taking a 7 day cruise, rather than a 4 or 5 day. Reason? The shorter cruises are usually on the older ships. Also, a 7 day cruise isn't much more than a 4 or 5 day. If you're flying, the cost of that is going to be the same regardless of how long you spend on the ship.