Given your comlete lack of experience, I would highly recommend that you do a few things first.
1) Take sailing lessons—An ASA 101 course for you and your wife, preferably separately. This will give you a foundation of skills to work from. Each of you should be capable of handling the boat singlehanded IMHO. This is a requirement IMHO, especially since you will have children aboard.
2) Take some time and crew on other people's boats, to get an idea of what kind of boat you're looking for.
3) Tell us where you are sailing and what kind of sailing you are planning on doing. Sailing on the local duck pond takes a different kind of boat than sailing on the San Francisco Bay, the Great Lakes or Buzzards Bay. Sailing short daysails might require a different boat than doing week-long coastal cruises.
It is going to be difficult to get a boat in decent shape that is above 30' for your budget. Not impossible, but difficult. Here is a listing of boats
in that size range... most of the lower priced ones probably have some serious problems.
I would also recommend you leave about 15-20% of your purchase budget aside for doing re-fitting, upgrading and modifications to the boat and equipment. Boats are not like cars, and one-setup does not work equally welll for everybody.
Do you understand what the annual costs of keeping a larger boat are going to be in your area? Marina costs, winter storage costs if you're further north, hauling costs, insurance, and miscellaneous maintenance costs all add up pretty quickly. Marina and storage fees alone can be $3000 or more, depending on the market. A lot of people go into owning a boat without a clue. It might make more sense to join a local sailing club initially... especially since you haven't sailed before.
Buying a boat is a rather large committment and if you end up hating sailing, can be a really expensive lesson.
Also, be aware that larger boats have larger costs associated with them, since the equipment is larger and more expensive, the boat is much bigger and many of the fees, like marina slip fees, haulout fees and such are charged by length. A 35' boat isn't 17% larger than a 30' boat, it is more like 60% bigger, since boats grow in three dimensions. A 30' boat is much more affordable than a 35' boat, especially to someone of limited budget.
However, I wouldn't go any smaller than 28' though... since the size difference between a 28' boat and a 25' boat is significant. This is especially true if your children are older, larger and more active.