Four cheap basses I have that I'd recommend highly:
Hohner B2 (My brother gave it to me about 1987). Huge sound, supremely playable and tiny.
Hohner Jack Custom V (£130 🤣). My only fiver, really easy to play but neck like an aircraft carrier when you first pick it up).
Westone Thunder (about £100). Sounds like a Precision, but more so...
Squier Jaguar Short Scale (bought new for £180, but now they go for about twice that s/h). Ridiculously lovely, fun and comfortable to play with one of the nicest neks ever (I A/B'd it with a Warwick in the shop, despite being several times the price the Jag blew the Warwick out of the water for playability). The J-pickup is a bit weak