I have 3 Squiers, never would have thought. My Affinity Jag H has a single MM style humbucker, a really nice neck, and is really fun to play. I upgraded the pickup with an EMG MMHZ, and it sounds really nice. The bass is really light, has some neck dive, all around is a nice instrument.
My second Squier is a Classic Vibe 70s P I picked up for a couple hundred dollars. I modded it with a Kickass bridge and a EMG Geezer pickup. I love this P. The neck is more like a Jazz neck, and is easy to play, it feels nice, the frets are smooth.
My last Squier is a Paranormal Jazz bass. I upgraded it with Seymour Duncan Apollo pickups, and this sounds fantastic. It has a great neck, smooth frets, everything fits. This may be my go to bass. What I really like about it are the controls - it has an individual stacked tone/volume for each pickup. Just tooling around with it the tonal possibilities are tremendous. I have a kickass bridge for it which is not yet mounted.
Two ways you could go here. One is to get a a Squier Classic Vibe Jaguar. It is medium scale, which is fun to play, and has the same stacked dual tone/volume controls as my Paranormal. This is really fun, but the prices seem to have gone up recently. My CV P and Paranormal are just as good as my Player Jag and Jazz without plek’ing. There aren’t many models with the dual tone/volume controls.
An alternative is to get a used Affinity Precision bass and through in an EMG Geezer PJ set. This would be easy and cheap. But it would not have the feel of a Fender Player, but it would be hella fun.