Easy money:
Unlock the GT40 Concept car from the Season 1 Official Races. You can buy it for $150,000 then sell it for $185,000 to $195,000. It only takes about one or two game days to sell it, for a $35,000 to $45,000 profit.

Quick start:
Get a six gear car. Top it out with the maximum HP, ten test it out in the Sega Drag race. Make sure you get your car in a Manual Transmission. Start out with sixth gear, and accelerate just before the last second. When you go up to 40 mph, shift down to third and make your way up the gears.

Super Racing Muffler
Clear the second season then race the hatchback event. If you raced the hatchback event before doing so, you may not perform this trick correctly.

After you clear the second season buy a Civic Type R 02 and fully modify the car. Race the hatchback event and come in first.

Nitros
Go to the used parts section regularly and check for question marks. For $1800 you can get a bottle of Nitrous Oxide, only for use in Drag Racing. To use it, press Y. Use wisely, as it is one-time only.
Note: This was done with a play time of 24 hours.

Nitrous Oxide Part
To obtain nitrous for the drag race you must be on a day ending in a 6 (26, 86, 236, etc). You must first lose a drag race at least one day before the day ending in a "6", or up to 3 days in advance (ends in "3").

Once you have lost, and it is a day ending in a "6", go to the used parts shop and the part will be all the way to the right under the "???". The part costs $1980 and you can only use it once (by pressing Y button) in a drag race.