You art humanoid.

Since Saiyans are stronger than most Humanoids and have wield over passive Ki, you have;
A Walk Speed of 30.
A Climb and Swim Speed of 20.
A Flight Speed of 45.

You know at least three tounges: Common and two of your choice. Knowledge of a tounge means you can talk in it, read it, and write it. Your class and other features might also give you tounges.

Saiyan Strength is stunning, but not so much thinking.
+2 to Strength and Constitution.
-2 to Intelligence.
You have resistance to Bludgeoning harm, which is halved thanks to it. 

All Saiyans have ape like tails. Your tail is 3ft long. Your tail gives +1 to Initiative rolls.
When foes wish to Tail-Grapple you must roll Acrobatics against your foes Athletics or Acrobatics roll, which if you lose you become Tail-Grappled.
When Tail-Grappled your movement drops to 0 and become Prone, you cannot do any Actions but roll to break the grapple, and all harm but Bludgeoning dealt unto you is doubled (Vulnerability).
You can wield your tail to Hang from and Grab things that are Small, and Swing 10ft in any direction from a reachable anchor as a Free/Bonus Action.

Your tail can be cut off with Slashing Attacks. To be cut off a foe must be within 5ft of you, or more if they have Ranged Slashing Attacks, and going after your tail. You must roll a Dex Save (14), and if you fail your tail is open to being cut and it has 3 + Constitution Modifier HP.

When cut off your Health, Speed, and Attack Damage are halved, and you art Stunned for One Turn. Your tail getting cut will take you out of your Great-Ape form forthwith. It takes 3 Days for your tail to grow back, unless healed with the Regenarate or Wish spells.

As a Saiyan, you suffer Vulnerability to Poison, meaning any Poison harm taken is doubled.

Thanks to Saiyan training you have (Blindsight) Saiyan Sense and can feel the Ki of others in a 10ft radius of you and behind thin walls (up to 5ft thick) with no cost. You know where living things are even if they are Unseeable, in Darkness, or you art Blind. You cannot sense magic (Arcana), Undead, or Constructs. You do not learn HP, or special qualities, only that something alive is near and where it is.

You can choose a feat of your choice. 

When you survive being dropped to 0 hit points once per Long Rest, be it by winning a Death Saving throw or being healed, the following effects happen:

You gain Advantage on your next two attack rolls or saving throws made before your next Long Rest.
Your next two attacks get a further 2d6 harm.

When you art reduced to 0 hit points but not killed outright, you can drop to 1 hit point instead. You can wield this feature once every Long Rest. 

Prerequisite: Your Saiyan has a tail.
When staring at a full moon (or a similar mighty energy), you transform into a Great-Ape. This lasts for 1 minute (10 rounds), or until you drop to 0 hit points, lose your tail, or choose to shift back as a Bonus Action.

Effects of the Transformation:
Your Size becomes Huge (20ft), but you cannot Fly.
Your Strength score greatens by +4 (to a maximum of 24) and hit points by an amount even to twice your Level.
Your Great-Ape Strike deals 1d8 + your Unarmed Strike damage and scales to 2d6 at Level 7.
Your Great-Ape Toss deals 1d12 + Strength modifier and scales to 2d12 at Level 7.
You gain Strength check and saving throw Advantage and can grab, lift, and throw Large things.
You cannot cast spells or do things that need fine control of body or speech.
If your tail is cut off, you forthwith turn back to Humanoid shape and suffer the drawbacks and cannot transform again until your tail grows back.

You can choose to not transform but must make a Wisdom saving throw of 13 or more. You can end the transformation early but must make the same roll.

Roar:
Once per every shift to Great-Ape you can Roar. Roll a 1d20 to find out how many foes in a 20ft radius of you must make a Wisdom saving throw of 16 or higher, or they become Frightened.