Monkeywrenchracing.com makes turbo kits for the Vibe 1ZZ and 2ZZ. You can look at those to get an idea of what you want from there. Garrett has this
https://www.turbobygarrett.com/turbobyg ... ostadviser" onclick="window.open(this.href);return false; handy tool to help you select a turbocharger made by them. It seems that the turbos used by manufacturers in production cars are cheaper and more common. For example, there's one used in like the Nissan Titan that I want.
There's also a supercharger for the 2ZZ Celica GTS, but it takes some modification to fit the Vibe GT and tons of modifications to fit the Vibe Base (1ZZ). Then there are the TRD/GM Performance superchargers, if you can find one, made for the 1ZZ as mentioned by the last posters. Not much modification needed for those to fit the 1ZZ if you have an '05-8 model. The SCs sound really cool, too. They SCREAM.
For front end sound improvements, you can do a cold air or short air intake, as well as the DC Sports header (4-2-1 design). The header that fits the AWD base Vibe is made by ABX and people have had issues with it cracking before.
For back end sound. you can go with the Magnaflow catback exhaust. There's also a TRD axle back, a Skunk, and a Borla exhaust. The TRD one runs like $700 when you can find it though, I think? I did a Magnaflow muffler and tip on mine for about a total of ehhh, $220 including having them installed and the parts.
EDIT: Oh, and MWR has
tons of other mods, including pistons and cams. I know cams make a different sound, no idea about pistons though.
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