What you need to think about is a 'tabernacle mast' setup.. still somewhat limited by boat size, but it's a way to, theoretically, at least, allow easy dropping of the mast for low clearance situations. As you might imagine this is rather common in the European canal system. Some images:
However it can be impractical or difficult depending on boat size, arrangement, and rigging used to accomplish this. Small boats are of course more manageable because the rigs are smaller, lighter, and have less leverage as they are dropping.
It's probably equally impractical to build a boat with a 14 foot mast.. even a 10 foot dinghy could easily have a mast taller than that. Gunter rigs might be doable, but again it depends on what level you want to get into sailing. Daysailing or eventual weekending and cruising?
The other issue that can arise is that, with your boat tied nicely in your back yard and the rig down, it's not a 'slip the lines and go sailing' situation and I think that would discourage usage to some degree. Are there sail-able waters your side of the bridge? That would be better if you didn't have to fiddle with the rig EVERY time you go sailing.
Having a boat in your own backyard is a pretty incredible situation to be in.. those of us paying moorage year after year get very envious. Good luck with how you decide to go..