screw the 3 ways....get sub better. and ur budget is actually alright.
my suggestion (not listing brands) get these parts
HU
2x 2channel amps
-1 for front components
-1 more bridged for sub
*try avoid getting 4 channel to power sub and comps... might have issued with amp cutting off due to not enough power or overheating.
* can try getting the brand prokick or agako for amps...good and cheap

6.5" 2-way component speakers for front
10 or 12" sub with enclosure.
this would give u a nice setup with good soundstaging.
the rear speakers if u have money to spare then get components or coaxial and run directly from HU. get 2-way oso... if no money then stick with stock speakers should be ok.
electronic crossover should get if ur HU has only 1 pair preout. but if got more than 1 pair then can forget about the e-cross...
as for shop....dunno ur location how to tell u which shop?