The Saiyan race is the most popular because they have the ability to eventually turn in to Super Saiyans. In terms of brute power, Super Saiyans are the most powerful in existance.
Saiyans that do NOT have Super Saiyan are one of the most powerful races in terms of just raw combat power. They also have very high zenkai (Total zenkai is your zenkai mod multiplied by your bp mod)
Saiyans can also turn in to Great Apes when the full moon comes out. But only if they choose to look at the moon. This will increase power for about 5 minutes til you turn back to normal.
To get Super Saiyan a Saiyan needs a certain amount of BP in between a random amount for each player depending on what class of Saiyan you are. Half Saiyans have the lowest requirements, Saiyans born with 1 to 10 BP has the second lowest, then non-Elite Saiyan, then Elite Saiyan have the highest requirement.
BP requirements for each Super Saiyan level for each class of Saiyan:
Half Saiyan: 500'000 to 700'000 for level 1. 72 million to 102 million for level 2. 450 million to 550 million for level 3. Can not go Super Saiyan 4 ever.
Low Class: 720'000 to 1.08 million for level 1. 102 million to 132 million for level 2. 360 million to 440 million for level 3.
Elite: 2.4 million to 3.6 million for level 1. The rest are the same as Low Class.
Regular: 800'000 to 1.2 million for level 1. The rest are the same as Low Class.
Super Saiyan is very powerful but it has energy drain while you stay in the form. You can decrease energy drain by mastering the form. You master the form by simply staying in the form. The first level of Super Saiyan can have its energy drain decreased completely.
There are 4 levels of Super Saiyan. Each has a higher requirement. Level 2 has higher drain than level 1, level 3 has higher drain than level 2. Level 4 is completely different and has no drain and completely different advantages and disadvantages.
Super Saiyan level 4 does not have a BP requirement to use it, it does require that you have level 1 and level 2 fully mastered. You do not need level 3 to use level 4.
To get Super Saiyan 1, 2, or 3, you need the BP requirement, then you either get 'death anger' from seeing someone die and you will go Super Saiyan. Some servers, especially RP servers, have it set so only the first Super Saiyan can get their form this way. The other way is thru inspiration, by fighting a Super Saiyan you will eventually get a message that you were inspired by them. After you are inspired you can go Super Saiyan just by getting regular anger, but it will most likely take multiple tries, and you will need 1.9x more BP than the requirement to do it this way for Super Saiyan 1, and 1.3x more for Super Saiyan 2 and 3. More anger mod increases your chances of success per anger.
You can also get Super Saiyan 1, 2, and 3 without the need for death anger or inspiration, if you have more than 3x the bp needed for SSj, 1.8x for SSj2, or 1.4x for SSj3, then you can get the form just thru normal anger. It will likely take multiple tries, more anger mod increases the chances.
To get Super Saiyan 4 you need an upgraded artificial moon, and Super Saiyan 1 and 2 fully mastered. Then you will go golden oozaru, and there is a chance you will then go Super Saiyan 4. It may take multiple tries.