I started out with a Venture 2-22. $2300 including the trailer. The boat floated, had a complete set of sails and after being cleaned and painted, looked respectable.
My aim was to learn to sail and do basic repairs. The boat did the job and I lived to buy a larger one.
I think you're on the right track. Given your geographic liability
there's only so much you can do.
You could theoretically "beach" a boat as long as it has a retractable keel. Some of the smaller Catalinas have this, some don't.
I would also add for after you find your boat: make sure that you have the required safety equipment for your state. Their boating website will have a list.