I am putting in a 100A sub panel , only using it with a 60A breaker from my house 200 AMp Service. I want to power my garage for air compressor and lights etc... Don't need much in the garage just a freezer, fridge, air compressor. I have been fine with one wire on a 15 amp fuse direct from house but am getting tired or tripping the breaker. I am a novice with the language.

Today I bought a 100A siemens eqL4100 4/8 circuit panel for the garage.
I also bought a 60 AMp breaker for the house. Double. I only need 60amp going to garage and this is the smallest panel Home Depot had at the time. 60 amp should be enough for my garage.

What wire do I need?? 120 feet.

On the sub pannel side I bought singles 15, 20 and a 30 amp breakers.

Attached or detached?
You need two hot conductors, a neutral and a ground. Typically for an attached garage 3-wire NM cable or SER cable would be used. I'd recommend #4SER if it is available. What I would do myself is #6SER and a 50A breaker.
If I may ask, what are you planning on doing with the SP30 breakers? There is no much you can do with them aside from a travel trailer receptacle.