I love turbos on 4 cylinder high reving light cars. BUT you are leaving off the larger fuel pump, injectors, fuel rail, water and oil lines, intercooler and of course a new computer to run all these things properly. Your stock driveline won't handle this kind of power either.
Why wouldn't you just go to nitrous or a supercharger for the same net lowend/midrange HP and less money? You can install a supercharger with underdrive pulleys in a day that is compatible with your existing systems. And there are no lag or heat issues. If you want the car faster remove weight.
To do this turbo thing right you have to lower the compression to allow for the high pressures up to 20psi developed with a big turbo(s). You need better heads, headgasket, pistons, rods, crank, oil cooler and a really strong block to do this. A stock block and headgasket can only reliably handle 6psi boost.
You must have way too much money.