If it were me, for home use, I would be looking for a second-hand Roland Cube 100 or Line 6 Studio 110 amp, both of which come with all sorts of effects/modelling already plumbed in plus MP3 play along/headphone out etc. Or, to totally maximise your money, Peavey combos sound great and are as cheap as chips. I practice at home with a TKO-80 that cost me £50.
Bass-wise, I'll make my usual suggestion of Westone Thunder bass or SGC Nanyo Bass Collection, either of which secondhand will cost you under £200 and are better than the Squiers I have tried or owned. There is high regard for Ibanez SR series on here, too, although I haven't ever played one.