Personally, I'm a big fan of Precision/Jazz configurations, especially my Squier Standard P-Bass Specials because…
1. I like the variety of tones I get. It can be pretty aggressive when paired with the right kind of strings (Mad Love for the Ernie Ball Cobalts, by the way!)
, but if I want a smoother/beefier sound, I'll dial the jazz pickup down to zero to get the classic precision tone.
2. If you're used to a Jazz neck, it's right up your alley. The body is a Precision, but it's got a Jazz neck.
Basically, it's a "best of both worlds" bass.
Now, the Standard series was discontinued a few years ago, but if you're not looking for a particular color-style, it doesn't take much looking around to find a decent used one. I have two right now. One I got as a refurb for $250 from an eBay vendor
and another from Guitar Center's used listings
for $125. More specifically, it was $100, plus another $25 for shipping and a one-year protection plan (it's my beater/traveling bass, so I wanted a little insurance).
If your budget is $300, and if this is something you're interested in, you should be able to score one somewhere online, hopefully without too much effort.