I would recommend this - a Harley Benton PB Shorty.
https://www.ebay.co.uk/itm/234081676825?hash=item36805aee19%3Ag%3Alm4AAOSwu61g5stH&LH_ItemCondition=3000
Currently @£42.87 with just under 2 days to go.
I bought one new a year or so ago for £80. Yes, £80. I had intended to change the pickup but, actually, the stock one is fine. Tuners arent the best but entirely functional. They are so cheap that it would be easy to dismiss it but - seriously - you could pay 3 or 4 times that - more, even - and not get a better bass. A joy to play, being short scale, and with flats it sounds like a good old vintage P bass.