Well, you are going to get a bunch of advise here. Looks like you are putting together a very enviable task, preparing for a life on the water with your family!
In general, being the opinionated person that I am, here are some thoughts to concider.
While there are many boats out there that satisfy your light cruising requirements, it''s the trans-oceanic part that will overide most other concerns. Construction and design will play a big part in this. In general, I have always felt that you need at least 40'' of boat to feel comfortable in the open ocean. Sure there are those who have done it on less (myself included) but the intimidation factor is somewhat lessened with a bigger boat. Plus, you will need something of sufficient size to handle all the stores and gear to make the trip enjoyable.
I prefer a deep keel for ocean passage, yes it limits your gunkholing, but as you stated, that is not a concern. I would tend to stay away from the cutter rig
, the extra weight and complexity is just not worth it. There are boats that have removable jack stays on a lever, but the ones that come to mind are out of your price range.
As far as construction, you want a robust vessel. Solid glass hull, thick with a strong bow. Lots of internal bracing, stringers and bulkheads fully tabbed into the hull. Chainplates that are tied into either bulkheads or a fastening system to the mast step/keel. I prefer a keel stepped mast, but there is nothing wrong with a deck stepped mast that is properly engineed for ocean passage.
The hull deck joint should be fastened with s/s bolts on 2" centers, with a hull flange in the 3" to 4" range. The keel should be lead, bolted to a robust keel shoe, and not encapsolated in glass.
Steer clear of the traditional "lines" with lots of overhang. It makes for a wet ride, deep slow motions, and reduces interior storage.
As you evalute boats, take a look from time to time at it''s PHRF rating. I know you will not be racing, but the rating gives you a good sense for a boats speed realitive to others. A boat that has a lower rating will be faster than a similar sized oat with a higher rating. Each point is worth about 1 second per mile in speed differential. As an example, a Bristol 40 rates 162, a Hinckley B-40 rates about 160, and a Tartan 41 rates 102, which is a bout a minute per mile faster. The Bristol and the Hinckley are very "Yachty" boats and the Tartan would be concidered more of a "Racer" (I personally would not want to put to sea in either the Bristol, not robust enough, or the Hinckley a little too robust) In an ocean passage, the Tartan would be DAYS or even WEEKS ahead of the other two, yet it is in the same size range. The Tartan would also be less work on the crew (although the large genoa could be a bit much to handle)
I choose the boats to compare because the Bristol and the Tartan are in a very similar price point to each other.
I would want a refridgerator, even if you are vegans, you can keep food so much longer with one. A well thought out electrical system, multiple battery banks are in order as well. I would invest in some of the excellent books on the subject of sailboat sytems, Nigel Calder''s come to mind. Read them and use the knowledge gained during your search.
Stay clear of in-mast or in-boom furling
gear. Nothing can beat the ease, speed, and simplicity of a slab or "jiffy" reefing system. While roller furling
/genoa make life easier for day tripps and port hopping, you may want to think about hanked on head sails. Less maintenance, never jamb, and the sail stays attached when it is lowered, a nice feature in a blow, catching "greenies" over the bow. And beacuse you will be passage making, the extra few minutes it takes to raise sails will not be an issue, and the ability to safely lower and change headsails in a storm will be greatly appreciated.
Self steering gear is also something to concider. I would avoid one that has been on the boat for many years and miles. I would rather want to install a new system of one of the more modern designs. Make sure your boat choice can easilty handle one if you decide to go that route.
You will whant to spend a little time finding a reputable marine surveyor, someone you can trust and work with. Listen to him/her when they make their recommendations.
Another reason I mentioned the Tartan 41 is that IMHO it suits you to a "T". The price is about where you want it to be. They are built like tanks and designed by S&S. Lots of room in a very well thought out interior. Although their dated CCA/IOR influenced design means you have a boat with a large headsail and small mainsail, they were far from the more radical aproaches to those design formulae. They are well built, and there are some very nice examples of them out there.
Hope you find your boat and enjoy the life you are choosing.
Good luck and fair winds.