From one newb to another, welcome to the forum.
I have been studying up on this exact same question. Here are the options I am considering.
Ibanez SR500 @ $550 (with active pickups)
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Ibanez SR400QM @ $450
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Squire Vintage Modified Jazz @ $280
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SX Jazz Limited Edition @ $180
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I am leaning towards the Squire Vintage. Great reviews. I am not sure there is much more "bass" for the money between the Squire and the Ibanez SR400QM. Also, I have read that the Squire VM is just a little better quality than the SX, but not by much.