It's your character, it's all up to you. Not everyone in that town has spirtual powers/medium training. Just thought I'd toss it out there.
However, I imagine youngsters from that down would commonly recieve either ghost or dark types as their first Pokemon, so your character definitely shows his heritage by starting with Gastly.
That might be the easiest route to take. And hey, if we think of anything later on down the line, we already have the basis for an explanation for it.