Welcome to the club! Congrats on the purchase, 04 STi's are great.
So basically most stage kits are as follows, generally.
Stage 1: Reflash ECU with either ECUTEK, COBB ACCESSPORT, or TurboXS UTEC.
Stage 2 is the Engine management system stated about with a catless or hi flow cat/Turbo back exhaust system.
Stage 3 Generally consists of the above stated with a walbro fuel pump, injectors, TMIC (top mount intercooler) and a protune
Stage 4 Generally is the above items with a new bigger turbo kit. and a pro tune.