Try the Normal Series with successivlely weaker cars. Get comfortable winning it with an NSX Type S Zero, and then progress to weaker cars--the strongest "Normal" (stock, unmodified) cars from each manufacturer, and then even weaker ones. [Note: the Normal Series is decidedly easier if the AI NSX does not show up; if a car beats the TRD only, that's different from beating the NSX ]
Try the Gran Turismo Cup (the alleged hard-tuned event in Gran Turismo League) with weak cars such as the Eunos Roadsters or the Demios or Civic del Sols.
Try the actual Hard-Tuned Series Special Event with an assortment of cars--try for ones which don't totally overpower the field. E.g. try an FC RX-7 or a non-turbo Supra. (e.g. SZ-R). I used to find the 180SX '94 Type X a good yardstick to help me remember how to drive that series, although now I think I need to find a slightly weaker yardstick...