I'd agree with the "try as many as you can" sentiment.
To be fair, you can't go far wrong with either a P or a J bass (or a P/J bass), and for that budget, you can easily get something that you can develop as a player on, as well as rehearse/record/gig confidently with.
Like guitars, they're all a bit different, and you really do need to try a good few out before deciding which one to buy (especially with that budget). Better to find one you have a "connection" with in a shop, than spend a shed load buying stuff on the internet and finding it doesn't work for you.
Good luck finding the right bass for you.