Well until Mark comes along, I will give my (less knowledgeable) opinion.

£250 is difficult, but just about workable.
Start with a good headunit, ideally Pioneer or Alpine. 3 pre outs is very useful (control crossovers from headunit, much to Marks disgust!

) Buy 2nd hand as you will get much better value for money. £100-£130.
Next you want a good 4 channel amp, at a very good price. Older V12 Alpine if you are lucky or Kenwood, Pioneer, Phoenix Gold QX series.
You don't need huge power, 35w rms x 4 is plenty. £30-£40
Sub and amp...
I personally prefer sealed subs, but Mark will say "you haven't heard a proper ported sub!"
(apart from the ones in his house that he designed and built)

Sealed is more compact (a lot more!), but requires considerably more power to achieve the same result.
I would say a 10" sub in a box can be had for £40 if you are patient.
I got a nice JL Audio 12" sub in a custom built ported box with a Phoenix Gold amp for £46. Just a question of patience.
Finally you need a wiring kit, most notably a LONG fused power lead and a splitter.
Most are 5m and that really is not enough. 6 or 7m gives a lot more freedom on placement.
I think I know his answer on "any system you wanted" in a car....
