The best thing to do is of course go to a music store to try them out, also keep in mind the kind of music you want to play on it. That will determine which route you want to go - you're fortunate to live in a time and age where you can find inexpensive basses of high quality these days.
Also another thing to consider, if you play modern metal/rock - do you want a five-string bass? Also do you want a passive or active bass? Active has greater tonal variety at the expense of sounding more well...modern. Classic rock, funk typically sounds better on Passive in my experience.
Some inexpensive brands I would recommend:
Passive
Squier P or Jazz. VM or CV
Yamaha TRBX174
Ibanez GIO GSR190
Active
Sterling SUB Ray
Schecter
Ibanez Talman TMB100, SR300
Yamaha TRBX304
There's many more of course - especially if you consider used instruments which I highly recommend. If you buy used, you can always re-sell them for pretty much the price you paid for it if you decide another bass would work better for you. Not only that, you can often find a better bass you wouldn't otherwise have been able to afford if bought new. You do have to be wary of what to look for in a used bass though, the condition, the neck, truss rod so perhaps go with someone who has enough experience to know what to look at. Best of luck and welcome to the low end.
