Well, if you're into modern, complex grooves and using bass to fill a larger tonal area, I think P bass is not the right thing to get. Precision basses are brilliant, but they're Basses with a capital B. So I'd feel jazz bass would be a better choice if you're interested in the fender style basses.
My top pick affordable basses are:
squier vintage modified jazz and classic vibe J and P. Standard stuff that playes and sounds a lot better than the price would suggest.
Yamaha bb414. P/J pickup config, well built, ridiculously good for the money.
Peavey grind series. Great neck through basses for the money. Update the pickups later on and drop in an aquilar or audere pre and you should be getting pretty close to your influences.
Those are all in the 300-400 range. For a little more you should try out spector legends, mtd kingstons and of course the fender style instruments that fall into the price range.
Also, remember to buy used. You'll get more bass for your buck. Some brands don't hold their resale value too well (peavey and carvin come to mind) and with these you can score a great bass for next to nothing.