I think I can be of a lot of "directional" help to you, in most everything you are talking about.
First, we have two boys (2 &5). The oldest has spent most of his life (since 5 days old) on a boat, and the younger has spent a considerable amount of his time on a boat. Most of our cruising (as a family) has been Texas and Florida and surrounding area. We lived aboard for some time and are about to head back to Florida again to do the same thing. I am currently finsihing up my house to go back. Anticipate my departure in the March time frame or earlier. Some of this will depend on the weather. So, with a very brief resume on my cruising life with kids, I will throw out a lot of thoughts and pointers. There is Nooo way I can cover everything, but this will get you on the right track.
First, boat choices. This is a very debated subject... especially on this site! So, many will agree and dissagree with me. Let me just say that many of my preferences come from boats that I have a very good familiarity with. However, many of my boat decisions have focused on how the family will survive on the boat without killing each other (which always seems more likely than any storm taking its toll!). SO, buy the fatest & most comfortable boat you can (that is sea worthy) - within reason. If you do not have kids, I do NOT NOT NOT NOT give this advice. Adult cruisers should buy the smallest boat they feel comfortable in. Now, as you look at boats, qualify them with a few very key questions:
1) Where will my kids sleep and how? THrowing them all together in a bunk is fine for the weekend, but impractical for long term. Most parents put their kids in the V-Berth or For'C'Sle, as we have too. Many times if you flip the mattress over, it has a split down the middle and you can run a divider board to split the 'V' in half. WHatever your personal decision is, you better have a berth that is safe, cushioned, seperated, and a nice escape point for one child to get away from another (or one child to get away from a parent).
2) Where will my kids play? This one will be a bit more of an issue for younger children (your age and my age) versus older kids. This will go against many passage-making boats where the salon is tight. You will want something wide open, maybe with a table that folds up to really give the kids a lot of space. Just look in the kids room right now at the collection of matchbox cars, building blocks, stuffed toys, etc. Now, not all of that will be able to go on the boat, but you better be prepared for a bunch of it to go. Where will you store them? THeir clothes? Where will they play with them?
3) Storage. You better plan on being able to stowe enough goods for 4.5 adults. Luckily, most sailboats have more room for dry goods and can goods than what is immediately apparent... but I have had to modify every boat I have owned (4 of them) to accomodate.
4) Escape Point. This one is the most important and is the most over-looked. If you have not lived abord with kids before, you will not undersatnd, but PARENTS NEED A PLACE WHERE THEY CAN ESCAPE TO WITH NO KIDS! The cockpit is not an option because it is often raining or it is cold or hot or something. This space on small sailing boats is usually in the owners cabin. Does it have a little chair or settee that you can relax in with a book? Can you stretch out? Can you close the door and block out everything? I am just telling you as someone that has been there, you better make this one a priority.
5) Cockpit. Again, think kids. Where will everyone sit? How high are the seats (for safety)? How will I run safety netting? How high are the stanchions/safety lines? In essence, it is not just how big the cockpit is, but rather how safe can you make it and how? In many cases, offshore boats are a good example of what to look for as the cockpit is typically safer and more protected than many of the cheaper, production, coastal-cruising boats.
6) Deck. THis is another compromise. Nice, wide cat-walks are ideal, but will eat up your space below. Regardless, you better plan on lots of extras on the deck (a second dink, unless you want to be stranded), maybe kayaks, water and fuel jerry cans, etc. Also, as I mentioned before, walk the deck and lean up against the stanchions and lifelines. Are they secure? Where do they hit you on the legs? Can you put safety netting on them? How will you run your Jack Lines? How will your tether slide from one point to the next? DOn't just look at it from an adult point of view. Take off three feet (get on your knees) and look across. Now, what do you see? You can also do this exercise down below.
7) Transom. I will likely get some dissagreements here, but I am pretty firm on one belief: I think ANY boat with kids on it should have a low transom that can easily be boarded. You can add a sugar-scoop to some of the older boats if you are stuck on a design that does not have a deck-transom... but you are probably better to keep looking for a boat with a deck-transom. Many, many of the passagemakers will NOT have this, FYI. THe reason is fairly simple: Kids will want to jump off the transom, board/disemb. by themselves, swim out back, etc. Not to mention, think about how you are going to get the kids on the boat in a sea (even at anchorage). More times than I can count, I have had the stern jumping up and down several feet with each wave while trying to help the kids get on. Imagine this without a deck transom... a real safety issue not to mention a bruiser.
8) Rigging. I have no real preference on this, but many parets like Ketch rigs so that they can let the kids manage the Mizzen Mast. I can see some validity to this argument, because you have to give the kids chores on the boat. Not just for you, but to keep them from being bored and to make them feel like they are a part of the crew, not a passenger. It will teach them a good sense of responsibility and they will actually have a lot of fun doing it. Now getting them to do the dishes, that is another story...
THose are the basics. Catalina makes a good boat and that is what we cruise on. I do personally like Catalinas better than Hunters, but some may dissagree. I like Jeauneau and Beneteaus too, but they seem a lot tighter down below to me and I do not care as much for the layouts. Thus, you might focus your search on a Catalina. There are better boats made, but the costs are considerably higher. Also, as it is an American made boat, getting parts and questions answered is pretty easy.
Well, this is a very long subject that I will not even pretend to tackle to any depth. Let me say this: It is much better than anything you can imagine, and much worse than anything you can imagine. The storms, the docks, getting groceries on the boat, being confined to 30-40 feet, cramped cooking an living... they are all realities. It requires you to be more creative. Take lots of dink rides. Make wildlife identification a game. Learn how to fish. Play lots of board games. Throw the TV in the trash and read books... a few of them together. You will be closer on a boat (litterally and figuratively) than you EVER were on land. But, it is not like weekends and vacation... it isn't all fun! Just do your best and realize that it will not be easy. If you work at it, it is manageable and a very nice way of life.
Cruising Budget and Costs
You mentioned 60k. You better plan on living aboard for a while and managing your money while working jobs, in my opinion. Our cruising budget is about 20k/year without boat payments. THat is pretty meager, honestly. That is a marina periodically, some shopping, periodic out to eat... but not a lot of any of them. We will mostly stay on the hook wherever we go. There are many people who can do it for less, and I salute them... but 20k seems a pretty reasonable number to me and the fam... especailly with 2 kids. You have three and will have to be more creative than I am.
As far as boat costs, what Cam and the others said is right: better budget a solid 100-150k for a boat, plus outfitting, then be surprised when or if you come in less. There are many ways to do this. If you want to pay cash, go ahead and that is the best way to go. But, there are some benefits to taking out a loan too: you can deduct the interest, you will conserve more of your cash, you can borry at historically low rates that (should they go up) may allow you to make more money if you invest wisely. The only big negative to a loan is that you are paying all the interest up front (like a house) and in 5 years of payment, you basically have not paid off any of it. Also, you have to send the payments in. You will have to set up residency in an apartment somewhere before you can take out a note, should you decide to do that. Most banks do not like liveaboards and I would not mention that it is your intention. Something about their money floating off into the distance and never hearing from you again...
ALL THAT BEING SAID,
It is worth it, at least to us. It is an adventure that almost all children and most adults will never have an opportunity to experience. It is not all wonderful, but you will change their lives in more ways than you can imagine. You have one life to live, live it to the fullest and help your kids to do the same.
All the best. Fair winds. PM me or write back with any questions.