RE: new bow for $350 or less - set up out the door what would it be?
I think Paul is right. If you'r limited to a budget of 350$ I personally be looking for a quality second had bow. You'd be suprised how many people trad in bows after just 1 or 2 years and this isn't a bad time to be in the market for one. IMO you would be ahead of the game going this route.
When I bought my first bow 12 years I bought a PSE Thunder Flight and hunted with it for 12 years. I spent near what you have listed for a max and got a great dependable bow. I will go on record as stating a good bow dosn't need to cost $600. The nova set up is a good start.