I'd look at getting something like a (possibly used) Squier Vintage Modified P Bass. Neat little basses and Ps can do anything!
This [url="http://www.ebay.co.uk/itm/Fender-Squier-Vintage-Modified-Precision-Bass-P-Bass-Gloss-Natural-Finish-/270968242296?pt=Guitar&hash=item3f16f74078"]one [/url]is about your price range, although there may be import charges applied to it as it's coming from America.