why is it have to been in that order?
Because those things maximize the effectiveness of the car by concentrating the money spent on where it will do the most good. Though I would probably put 'suspension' ahead of 'drivetrain' in my list.
Tires are the interface between your car and the road. Good tires will maximize the performance of the car in any state of tune, and bad tires will cripple a good car, in any state of tune. Always buy at least T2s (super slicks). I never go softer than T4s (medium slicks) because they do not last long enough in races where tire wear is counted, and I do not want to get in the habit of relying on the extra grip of softer tires.
Weight is the enemy.
All of the stock systems in your car will do a better job, if they have less work to do. Their 'work' is to haul the mass of the car around the track as quickly as possible. If they have less mass to haul, they can haul it more quickly. I always do at least Lightweight 2 on any car that is not required to stay stock.
Suspension is second only to tires, and is the next link in the chain between car and road. Suspension allows you to use speed efficiently by maximizing the amount of grip the car has. More grip = faster corners = faster laps. A great example of this is Gil, who beat the Monaco Enduro using the piddly little Lupo Cup car. He was at a large power disadvantage, but he could carry a much faster average speed through the turns - giving him the win over much 'better' cars. I ran the Clio racecar at the Seattle Enduro, and beat the Corvette Z06 and Viper GTS by 2+ laps. I had less power, but I was able to use it better thanks to the car's handling.
Drivetrain is important because it is the largest part of how to get the power to the ground. Most cars in GT3 have plenty of power, and it is a matter of using it well. It also has effects on both ends: in traction (LSD and gearing) and in power (gearing and clutch/flywheel/driveshaft). Note that adjustable gearing - the racing transmission - is effective in both of those examples, which makes it the #1 drivetrain priority.
Power comes last, because it is dependent on all the other systems for its effectiveness. Everything else determines how efficiently the available power is used, so they should be up to the task of handling the
stock power output before you ask them to handle more. To get the most out of the car, get everything else working properly before adding power - because then you
also get the most out of the extra power.
Many people cut right to the power mods, because they hide a multitude of other problems in the car, and in the driver's ability. Enough power overkill can beat the Beginner and Amateur races by brute force. But that won't help on the Time Trials and License Tests, where the cars are stock, or on Professional series, where the competition AI cars are maxed out as well.
Good luck. And welcome to GTP! Look around, and ask questions. There are a lot of knowledgeable people here. Check out Der Alta's writeup series, and also at the tunings board.
