With your post punk interests i would definitely get a precision. The sound and look will get you through any musical situation in that context. Given your cash restrictions I would recommend continuing asking for info and keeping an eye on the sale board here until something comes up that matches your budget from a local board member. 250 is not a huge amount to spend but a good Mexican fender or parts built precision could be yours and will work perfectly well for practice, rehearsal, even recording, especially if the pickups are upgraded down the line.
Soundwise, I would suggest a cheap but punchy second hand combo for home practice, rehearsal and small scale gigs. Bigger gigs you could rent back line or borrow from other bands (make sure you ask in good time before the gig!). You will also find that some board members will get rid of old dated, combos for around the 50 quid mark as they are difficult to sell. Search the amps classifieds here for 'combo' and you will see what I mean. Getting something that is in a functional state by peavey, ashdown, ampeg or trace elliott would be my recommendation. Again, you're not looking for the best amp in the world, you just need to make a fairly loud noise and for it not to break down
Cable, straps, strings etc can be sourced through board members here as well either as secondhand cheap or freebies or high quality, independently made merchandise (OBBM leads are excellent).
And yes, get a good set up. Find a local guitar tech through the board who can give the new bass a set-up. But if you buy second hand from someone who knows what they are doing, they should ensure the bass has the correct set up and would have set up the action/ relief on the neck properly.
Good luck!