The Kenner Privateer would not be my first choice as a boat, given the sailing you're planning on doing. Have you sailed the boat? If not, what boats have you sailed??
Also, define medium sized lake. Lake Winnepesaukee in New Hampshire or Lake Champlain in Vermont/New York are medium size lakes if you're comparing them to the Great Lakes, but otherwise would probably be considered large lakes.
There aren't many benefits to buying a ketch rigged boat in this size range. In a larger boat, it often makes sense since it reduces the size of the individual sails, and allows you to have a few more options in balancing the sailplan of the boat for various wind conditions. However, in a >30' boat, the mizzen mast takes up a lot of space and adds a fair bit of complication and maintenance expense to the rig that isn't necessary in a sloop rigged boat.
From what you've said in your first post... you don't have a lot of experience sailing, you probably don't have much experience with the different types of boats or rigs, and you're basically acting without knowing what the hell you're doing.
You'd probably be much happier in the long run with a different first boat. A sloop rigged boat would be easier to handle. A more modern design would handle better and sail better, and do so in less wind than the Kenner would generally require. A Catalina 25, a Hunter 25, a Ranger 26, a Cal 25, an Olson 25 or any one of a hundred others would be far more suitable and less expensive to own IMHO. Also, any of these would be far more enjoyable, in terms of their ability to sail and handle easily, especially for a novice sailor. Some of the boats in this range are trailerable, and would allow you easily move the boat from lake to lake, as well as simplify your winter storage situation.
Personally, I would recommend that you go sailing on a few more boats and learn to sail a bit better before biting the bullet. If you really want to jump in feet first—by all means, do so, but look for a boat that is a bit better suited to your needs as well as a bit better in terms of resale value. In many cases, your first boat isn't one that you keep all that long... you'll get three-footitis and want to sell it and get a bigger boat or a different boat. Getting a boat that holds it resale value will make doing that far easier.
Don Casey points out in his book,
This Old Boat, that the first boat is often just a way to learn about what you really want in a boat, and that the second boat is often the boat that a person buys and keeps for years, based on what they learned from their first boat.
Also, if you have any friends that are experienced sailors, and trust their opinions... you might want to see if they can come with you when you're looking at boats. You also will probably want to get a survey on any boat you are thinking of buying....but getting Don Casey's
Inspecting the Aging Sailboat, will at least let you take a basic look at any boat and see if it is even worth bothering to make an offer on or get a survey for.