New member, here's the story

I've played guitar for many years, now, my workplace put together a music room, and when I went to check it out, I picked up the electric bass just on a whim (can't ever recall touching a bass before), and here I am

So I'm thinking of throwing together a parts bass (I've built electric guitars from parts, from scratch, etc.), I see that both P & J bodies are plentiful, would either of them get in the ballpark of something like this tone (putting aside question of amp)?