The list of good basses around the $300 and less mark is quite extensive.
There are none that I would place on top of the list in particular at the moment, but there are many that will get the job done, and do it at a pro level.
As for what has been suggested so far, the Squire Vintage Modified is an excelent choice, as is a used G&L tribute. Especially if you can find a used L-2000 (good luck though).
You can get a new:
Epiphone Thunderbird for $300
Squire Deluxe with active pickups $300
Peavey Millenium AC (active) BPX 4 string $300
You can also find Trabens and a few good Schecter basses in your price range. I'm not an Ibanez fan, but you can also find many that will do you a good job.
I would gladly own any of the basses I listed. In fact, I own a Peavey Millenium AC BPX 5string and have gigged with it. In fact, I have tossed a couple recordings down with it, and it does great.