The 8250s are the ones that come on new American Standards. Well I know that everyone is different and strings are subjective, but I just bought a new MIA Standard Precision V and the strings that came with it were some of the worst I've tried in a long time! They have these awful overtones that are almost as loud as the note itself! I was actually worried that the bass was defective! It was so bad that I refused to play the bass until my string order came in. After I loaded my new strings, the bass sounded great!
You can find plenty of other string brands that will work for what you've described (even better than Fender). Here are some that I've tried that will work for classic rock and jazzy stuff (not including flats because it sounds like you prefer rounds):
-DR Lo Riders
Those will definitely work, and I'm sure other people can suggest strings, too. But if you must go with Fender, good luck.