Is a 60A sub-panel adequate for my workshop/garage?
Typically you use 6 AWG copper wire for a 60A run, and 1 AWG Aluminum wire for a 100A run.  Between the two, #1 aluminum is actually cheaper, though it requires more expensive conduit if you use conduit.   (using conduit can be a convenience; Rigid conduit only needs to be trenched 6" of cover instead of 24" for buried cable, and Rigid provides a valid ground path, so no need for a ground wire). 

The welder could surge 50A, and if the compressor is running at that time, these could peak the circuit past 60A.  This will not immediately trip the breaker, but it could cause minor voltage drop.  Rather than be in a situation where the circuit is straining at limits during welding, I'd advise erring on "large".  It certainly does no harm. 

Speaking of "large", we recommend large service panels.  The welder will need 2 spaces, as will any 240V load.  If you put together a respectable 240V workshop, you start blasting through spaces 2 at a time.  Dealing with an over-full panel is much more expensive than just buying a bigger panel in the first place, so we recommend a biggie. And it's perfectly OK for the panel amp rating to be larger than the feed breaker.  Some people think if the breakers are equal size, the one in the shop will trip first - doesn't work that way. 

And by the way, you don't need a main breaker in the subpanel.  However you do need a shutoff switch if the subpanel is in an outbuilding, and getting a panel with a main breaker is the cheapest way to do that. 

Also, because it is an outbuilding, you need two ground rods at least 6' apart.  You can do it with one ground rod if you do an impedance test, but setting two ground rods is easier.  Despite the ground rods, you still need the ground wire back to the main panel (or Rigid conduit will substitute). They have different purposes, both important.