Hi wintermute. I'm no expert, but my wife and I enjoy an Old Town Loon 16' tandem. We do all flat water/lake/touring type stuff. The boat is plenty big enough for us an camping gear for a long weekend. The Loon is a recreational kayak. We went with a recreational boat rather than a full-blown tandem touring boat because of cost and us not being sure how much we were going to use it. Though not as sleek as a touring boat, the Loon is still faster and far more stable than a canoe. Ours has a rudder, which helps a lot on wnidy days.
We looked briefly at sit-on-tops, but they didn't seem to offer the cargo capacity as a sit-in boat did. Also, we felt the sit-in boat had more room if we were to add a child into the mix. That was the thinking back about 6 years ago, and now we have a child who we'll most likely get out onto the water next summer. Another reason we went with a sit in is that you can fashion a spray skirt to the boat. A spray skirt is really nice when one is facing rough water or bad weather. In both cases, the spray skirt will help you stay dry and warm.
Since you are looking to invest in multiple boats, I suggest first doing research and narrowing down a few different models that may be in your ballpark as new boats. Whereas your 12y/o can probably handle her own boat, I would plan on having the 5 y/o ride with you and your wife. At 5 y/o, she most likely won't have the speed, endurance, or boat handling proficiency to keep up with the rest of the family unless you're on a very short trip. You could also get a second single that the 5 y/o can eventually grow into, which you or your wife can pilot, and the 5 y/o can ride in the tandem with an adult until she can manage her own boat. Getting two boats now rather than three will be easier on the wallet, too. Also, consider the safety factors of having your 5 y/o in her own boat vs. having her with you in the the tandem.
Once you decide on what boats you think you'd like, check out the used market. If there is an outfitter somewhere near you (REI store, or any place that rents kayaks), inquire with them, as they sell their rental boats from time to time. Shopping for used boats may not always yield exactly what you are looking for, so you may have to be flexible with what you can get.
We are really happy with our Old Town boat. I think Old Town offers very good value in their boats. The have a broad range of products from simple rec boats up to sleek touring boats. I'd very likely consider getting another boat from Old Town if I was in the market. Necky and Wilderness Systems also make singles that I would consider.
Good luck with your kayak quest!