Why can't an airplane be little? There is even a company, Little Airplane Productions.
"Little" has been added sometime in the last three years :-) .
Is "small jet" possible?
Too specific. Sure, it may be the most probable nowadays, but maybe he's buying an old plane from a museum that isn't even supposed to fly ;)
"jet" is "odrzutowiec" (or "samolot odrzutowy")