I personally like the Versa. I am not aware of any Versa's or Fit's running in NASA's Time Trial series though I will know for sure in Feb. I believe they are running in some special tuner series which is basically for big dollar tuning companies.
That Versa by the way is not boosted.
As for what class the Aveo is in, well right now it's in TTG but with boost it would most likely end up in TTF which is where my MazdaSpeed Protege currently is.
If I could get any form of financial assistance, I would love to campaign a boosted Aveo and could probably do quite well with just a few basic mods. 15" tires and wheels, 150whp, H&R springs, Drivers seat, Tunnel Brace, front lower tie brace and some fender braces.