You know, since the summer I've thought about doing lots of things to my car and one of them was a turbo, but what's the point? When you really break it down, it's an economy level car. Also, when you get into performance mods on your daily driver you can count on not driving for weeks at a time. Another thing is, a lot of parts on the Aveo are made cheap, so adding a turbo and all this other stuff means you'll be going deeper into more parts, and trying to find stronger non OEM replacements.
Another thing, if you have the money for the Aveo and want something you can tune and make fast and what not, join the dark side, sell the Aveo and grab a Civic. Hate to say it, but any part you need for a Civic you can get pretty easy and pretty cheap and the older Civics have huge lists of aftermarket parts that you can buy, thanks to The Fast & The Furious movie which really brought out the Civics true potential.
Keep the Aveo, get an older Civic like a 2001 isn't bad. Put some money into it, turbo, cold air, fuel management, blow off, performance struts and shocks, body kit, paint it e.t.c get the whole thing going. Then you'll still have a car to drive daily while your toy is being tuned.