+1 for try as much as you can to find out what you like. Some basses are extremely heavy, some are extremely lightweight, some have fat necks, some have skinny necks - not everyone can get on with all types.
In broader terms, if you pay £300 for a secondhand bass you will get something that is good enough for absolutely any situation. Some makes/models are unpopular at the moment so if you aren't a concerned what is written on the headstock you can get fantastic bargains - SGC Nanyo Bass Collection basses go for next to nothing and are superb quality. I recently bought a mid 80s Yamaha RBX800A for £150 and it is just as good. I paid a lot more for a Fender Precision Lyte and it is no better, frankly. Westone Thunder basses, in their various guises, represent incredibly good value for money - £300 would probably get you a Thunder IIIA, which would give most £800 basses a run for their money. Somewhere in the for sale section there is a MIJ Fender Precision for £225 - but scruffy but an absolute bargain IMO. Lots of deals to be had - a buyers market at the moment but it helps if you know what you want.