Get your car into the 400's at the wheels
Few ways to do it and be reliable and fast at the same time, and NOT spend all of your 3k.
Buy my used bolt on Turbo, 550's and Lexus meter. IT works fine on the stock TCCS, but you will need to buy a areomotive adjustable fuel pressure regulator. (Sold on here by a few folks, and they are worth every penny.)
Get yourself a good wideband to tune with.
(Shameless sales pitch, but really it would be a good upgrade path for him at this time. Live with 420rwhp for a few years, and then if you think you need more, buy a larger turbo and go the route I'm on now shooting for the 600+mark.)
Your going to need brakes and other stuff before you head out for 600however
(If you want to come home alive that is.)
My turbo would run you about 2k if you buy a new one. Fuel will run you 300 for the injectors or more, and the Lexus is 150 used at the salvage yard with a sensor. All you need after that is a DP which will be EASY using the parts I'm including with the turbo setup. (It has the flange and a short pipe, you just add your DP to it, or make one, or have one made, and then choose the cat back exhaust of your choice. )
Put a Walbro pump in the tank, and your good to go.
So, 1000 for the turbo
275 for the injectors
100 for the Lexus.
450 for the cat back from your choice of sources.
95 for the Walbro. (Again from the many sources out there.)
250 for a Areomotive AFPR setup.
Remove the J tube, do some simple mods and your pushing 420 at the wheels on pump gas man, and have some money left over for larger sway bars, wheels/tires/brakes and other fun stuff like springs and struts.
Sorry in advance for the shameless plug for the stuff I'm selling, but you asked for the low cost way to do it, and I'm offering an option.