Dont do a single GT28R you will surge it.
1JZ at wot 7000+ rpms will pull more air then that little snail can handle.
Drift motion haves bolt on kits you should buy a package from them.
If you want very close to oem performance with the least lag & money spent put into it leave the stock 370 injectors in it.
Buy a GT30R boost up to ~13psi on stock system just put $120 in a chinaman manifold ~$300 cheapo turbo $120 chinaman downpipe $400 custom 3" exhaust.
good for about 380whp 440s/fuel manament and a little more boost could get about400 ish
Now if you want a slightly better setup grab 550s+resistor pack + AFC like a neo for fuel manament 100 for walbro or 200 for dual walbro.
GT35R along with the rest of the supporting mods 500-600whp with a good tune. you will need a clutch better braking system etc you have to stop eventually!
Remember when going from a small turbo GT30R to a medium turbo GT35R Lag is just a shift away so having 10% low end usage but gaining 140% power in the 90% of the power range is not a bad trade off.
you can compensate for lag other ways like twin charging dual bearing twin scroll turbos GM automatics lower final gear etc.. so lag isnt an end all when using a medium turbo.
Large turbo you should even think about it just buy a 2jz and get a sponser etc..
I think in your situation just grab the gt30r like this one
http://www.atpturbo.com/mm5/merchant.mvc?Screen=PROD&Product_Code=GRT-TBO-005&Category_Code=GRT
.82AR
Vband 3"
T3 divided housing
internal external waste gate is up to you I perfer external but I have a medium turbo setup for simplicity you may want internal?