Is your AVI source really progressive? Never-the-less, set your project properties in Vegas to match your source and render to your desired format. Be sure to set the interlace method to interpolate in project properties if your source is interlaced, otherwise set it to none. Set render quality to best.

You may be able to get somewhat better quality using involved procedures that have been discussed endlessly in this and other forums since HD came out and the need to convert from HD to SD and vice versa.