A 500bhp capable turbo on a 2l 4cyl engine with no/little lag and fast spool is a unicorn.

.

I.e it doesn't exist, unless you're using nitrous to spool it up.

There always has to be a trade off.

If you want response, spool and a punchy, fun street car then you want something like a gtx2871r

(or similar) and

'settle' for something like 400bhp max.

If you want a peak power monster then you'll need a big turbo that won't choke the engine but will take longer to get going.

If you really want 500bhp with loads of torque and instant throttle response then you need something with a Bigger engine

- like a LSx V8.

Decide what you really want from the car

- peak power or response, then choose a turbo.

That said, you need to match a turbo to your engine, select a compressor wheel that flows enough lb/min to support your power goals

(1lb/min per 10bhp is a general rule) then choose the right hot side to drive it

(e.g, probably something with a

.82 exhaust housing for 500bhp)