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If your standalone is able to read AVI file, you don’t need to convert the movie into a different format. So, you can burn the file on a CD.
Convertxtodvd is an excellent software. Probably the stuttering issue was caused by a low quality disc. If the movie plays good from the HDD, then the culprit is the burned disc. Try again to burn the converted files on a quality disc like Verbatim, this should solve.