Instant only happens with a blower but that robs HP.
The smaller the turbine wheel (exhaust wheel) and housing, the sooner the spool up (dependant on the engine displacement of course), the larger the compressor wheel and housing, the greater potential for higher boost. There is of course a balance between the two, and this depends on what type of driving you're looking to do.
My turbo in 4th, starting at 1000 rpm sees 1-2psi instant when I push the peddle down, as the rpm's climb, mine sees 5-6psi by 1500rpm and 12-13psi at 2000rpm. If I'm cruising at any speed and I'm at or just over 2000rpm and put the peddle down, It'll jump to 16-17psi then my engines exhaust pressure opens the flap on my internal waste gate as the actuator spring is not powerful enough to hold the flap closed for any more than 14psi. Now, my actuator arm is also pretty much maxed out so that even if it has opened from seeing 14psi, the waste gate flap is not fully open and more of the exhaust pressure is spinning the turbine, which in turn increases my boost output from my compressor. If I had an external waste gate, I'd be able to set it for 14psi and I wouldn't have the fluctuations due to a week actuator spring (or I'd just learn to be happy with 10psi and call it good, but that ain't gonna happen

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General road driving with highway performance (what I was looking for) wants to see (as Dougal mentioned) max boost reached at cruising speed (mine is 2100 rpm at 100km/hr) as when you see a hill, you can hit the throttle and your turbo should max out and offer the power you're looking for.