I picked up a new Fender Tele style "P" bass a year or so ago. It's a love hate relationship, it plays great, sounds great, but weighs a ton and is not a contour body. It has a great stage look, so it has become my gig bass. The model is no longer available, but I'm sure there are some used ones around. My recommendation is to play them first, through a similar amp that you will be using. Only you will know what fits you right, and that might take some time.
I've always loved the ZZ Top, Dusty look and this Tele was only available online so I took a chance. I usually like thin necks, but this one has a baseball bat and love it. It will stay in my collection, though I may order parts to build a similar bass with my own specs (lighter and contoured body).
Good luck on finding your next axe...
https://www.musiciansfriend.com/bass/fender-standard-telecaster-precision-bass-limited-edition
Look's killer. Might have to get one. The ones I'm looking at now have P/J pickups.