Should I buy star tip extensions for my ratchet or just the Allen key type set?

Allen is different from Torx; both are necessary.That means you need both tool sets to properly work on equipment.

I assume that when you write "Allen key type star tip set" you mean those L-shaped Torx keys.

Both work, it only depends on your preferences.

• The L-shaped keys are a good compromise for a tight budget, but have their drawbacks as you can only use them directly on the location of the bolt. So no extension, no ratchet, no torque wrench and no impact gun.
• The socket extensions are, in my opinion, fine for larger bolts (>=6mm). You can combine them with an extension, a torque wrench, a ratchet or, in case of the impact sockets, an impact gun.
• Another alternative, not mentioned by you, are the screwdriver-style Torx drivers. Those are preferable for the smaller bolts, as you won't be able to turn larger bolts, but allow very comfortable wrenching on the smaller ones.

I, personally, prefer the more expensive solution: Sockets and screwdrivers. After all, if you expand your hobby you need every variant: The larger sockets, the small ones, the female Torx variants, the long extended ones, the ability to attach a torque wrench, perhaps one fine day you buy an impact gun.

Picture: My Torx collection.