OP, the tone you want is a high-mid grind.
There are many ways to get this. Basically the only requirement is a set of growly roundwound strings. Rotosounds, D'Addarios, GHS Progressives, and many others will work just fine.
A P bass, stingray, G&L L2000, Peavey T40 or Cirrus, Wal, and many others will all get you there.
Specific amps aren't critically important either.
Basically, you want to cut out 200-500 hz, a.k.a. all the "low mid" frequencies. Drop those by a few db. Boost from 800-1.5k hz (high-mid frequencies). Leave the treble alone. You want a decent amount there, but you'll get it by default from the roundwounds. You're not going for slap-tastic sparkle, so you don't really need to boost it. Depending on your bass/amp combo, you might need to cut some low end out, or leave it be. Don't boost it though.
An overdrive pedal is optional. If you like the sound of a particular one, go ahead and use it, it can add some nice high-mid overtones.