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I think your first step would be to set a goal. Which type of "road racing"? Autocross, track, etc? What you want to do should determine your goals. Assuming by road race, you mean track
, so really it depends on how much power you want, and your budget.
You can keep the same motor, build it and turbo it. Just keep in mind that motor really was deigned for fuel economy. For more oomph and more $, you can swap the motor and turbo that.
This is also assuming the car is manual -- if it's not I would not recommend any major modifications.
Look into B-series swap, K-series if you have a little more $ to play with. Expect a turbocharged Civic done right to cost you at least $3000, maybe $500 of that should go towards tuning. The tune is THE more important part of any turbo setup -- do not cheap out on it.
Take a look at
THIS LINK HERE. -- I post this quite often here on the forums. I consider it to be a (slightly outdated) bible for boosting a Honda. Plenty of important information in there!