Cheapest way to get a compact crank is to find an older mountain bike triple (110/74 bcd) and run it as a double "compact" crank. If you get a shimano triple, it may well work with your existing bottom bracket.
Same for the rear derailleur. Best bet is to find an older rear derailleur from a mountain bike like a Deore. That can handle at least 32 teeth in the rear.
If you want to go new, you don't need to spend a bomb. The cheap Shimano derailleurs are fine (like a Claris). FSA makes square taper 110 bcd cranks that don't cost a lot and will work just fine.
Still you are talking around $200 in parts not including labor.