You have unrealistic expectations.
Budget more, or lower your expectations. If you ask around long enough eventually you'll realise what's realistic for the budget. A few of the guys have already stated this.
300kw means you'll need a very expensive setup to make it responsive. And yes, a big turbo is needed for that power. And big = lag.
With a good setup you could make the power cheaply with the KKR turbo, but it won't be as responsive as a more expensive ball-bearing turbo, or a smaller turbo.
If you want a turbo to make 250kw with plans to go to 300kw, you'll need a big turbo. Because you won't be pushing it to full capacity at the lower power level (less boost) and you need supporting mods before you can push it, you'll be experiencing plenty of lag until it's potential is used
I'm sure you can get what you're after. Keep researching and GL.