As stated previously you will have to decide on what power you want and how much you want to spend.
You said for starters, you would like 400-425 whp, so I take it by that you mean that eventually, you would want to increase that.
This is why you have to decide from the get-go what your goals are because supporting mods can be very expensive and these mods would require upgrading when you jump from 400 hp to say 600hp.
If you want 500 hp with similar torque then you will also have to go fully forged.
I do not think that you have a solid understanding of what is involved here.
For your budget mentioned of 4k, the supercharge is your only option, but again that will be a struggle unless you find a good preowned kit and you can fit it yourself, but it will still require tuning and mapping so budget in a grand for that alone.
Upgrades to chassis, suspension, brakes, fueling, tyres, etc. etc.etc will be another five grand.
Add in another grand for coincidentals and 3 grand for your insurance and you are at 14k at the blink of an eye.
For a safe 500+ whp, budget for spending 25K+ for the TT kit and proper supporting mods.
My DE 350Z is putting down 720bhp at the wheels and circa 680 lbs ft which I have loved modding over the past 14 years but no matter how fast it is you are always looking for more, the car is very quick and is so well planted for circuit fun, however, there is a huge ongoing maintenance responsibility as stuff breaks all the time and unless you are hands-on it is not cost-effective.
Perhaps in the cold light of day, it might be a plan to stay n.a. for the next couple of years and get your brakes, suspension, chassis and tyres sorted and build up your pot of cash and your insurance NCD and then revisit the idea in a few years time.
Here is the link to the f.i register: https://www.350z-uk.com/topic/66265-official-list-of-uk-fi-zeds/?tab=comments#comment-983531