Check with a California tax attorney. The last time I checked, if you
buy a plane out of state, then keep it based out of state for 90 days
and use it out of stat and can prove it (tie down reciept, gas reciepts
logbooks) you don't have to pay the sales/use tax. It doesn't have to
stay in the state where you bought it. You could buy it in Ohio, fly
it to Nevada and base it in Las Vegas for 3 months, fly it once a month
there. Might be worth it.

Another option would be to lease it for a year.

A 150 is a great choice. You can sell it for exactly what you have in
to it, knock of $500 and you can sell it in a day.

I wouldn't teach my own kids to fly. I'd find a CFI that I liked.
There's too much relationship baggage between a teen and a parent. YMMV