For what i imagine to be your price range, just pickin it back up, I'd look into Squier and Ibanez.
Squier: Look atf their Affinity or Vintage Modifed Jazz/Precision basses. Go Affinity if you want to save more money; however, the Vintage Modified series is widely held as Squier's best line of basses, and one of the best basses in a lower price range. Their Jazz basses are really versatile, and can sound good in almost every style of music. Precisions have a great sound for Punk/Rock, but aren't as flexible.
http://bass-guitars.musiciansfriend.com/product/Squier-Affinity-Series-J-Bass?sku=519631
http://bass-guitars.musiciansfriend.com/product/Squier-Affinity-Series-P-Bass?sku=510424
http://bass-guitars.musiciansfriend.com/product/Squier-Vintage-Modified-70s-Jazz-Bass?sku=519639
http://bass-guitars.musiciansfriend.com/product/Squier-Vintage-Modified-Precision-Bass?sku=519638
http://bass-guitars.musiciansfriend.com/product/Squier-Vintage-Modified-TB-Precision-Bass?sku=519758
Ibanez: Try something from their GSR line, like the GSR200. There's also a version of the GSR200 with a Flamed Maple top if you like the look better, go for it! The GSR line is like a cheaper version of the SR line, so it shares some of the same features the necks are really slim and comfortable to play; these basses feel really nice.
http://bass-guitars.musiciansfriend.com/product/Ibanez-GSR200-4String-Bass?sku=519524
http://bass-guitars.musiciansfriend.com/product/Ibanez-GSR200FM-4String-Bass-Guitar?sku=515059
The most important thing is to play the bass yourself before you buy it. Go to a music store with a few in mind, and play all of them. Find which one feels the best, sounds the best, and suits your needs the best then you'll be set!
Hope you find what you're looking for