First Post - Looking for Advice on Trailer Sailer

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Hello to all,
I am starting to look for a trailerable sailboat for the wife, 3 small kids, and myself. We will be sailing offshore and intercoastal in Florida as well as trips to the keys and possible lake trips.
My parents owned, among many sailboats, a MacGregor 25. I found that boat very easy to launch and trailer, but didn't care for the 'light' feel under sail. This was in stark contrast to the feeling that really hooked me on sailing which was sailing a 30+ foot racer, no idea make, through deep swells while the rail was under water...
I get that that kind of sailing will probably be difficult in a swing keel boat.

We are looking at a Catalina 22 for our first sailboat due to its easy trailering characterists (size, weight, and swing keel, price), but am concerned that offshore it simply won't be enough boat.
[I am also concerned about getting something big right away due to convincing the wife that she really would like sailing....]
We will need a boat that will be launched and retrieved frequently, so stepping the mast easily is an issue.

I think my other option is to get something in the 25 to 27 range with a shoal keel but the easily launch and retrieval will probably go away, yes?

My tow vehicle is an F250.

Oh, one more thing, I am doing this on a seriously small budget, <5k, so probably 70's and maybe early 80's boats.

Eventually I will make the switch to full keel cruiser, but not yet.

So, does the cat 22 sound like a first good step?

About my username, it is sort of a joke on myself being a former ship's engineer. mma94