We have a 100 amp main panel, range and dryer are gas. Neutral and ground wires on same bar. I put in a 60 amp breaker and ran 10/3 to shed in pvc pipe. Bought a 125 amp panel for shed/workshop with a separate ground bar. Red and black go to main breaker, neutral and ground go to separate bars with a ground wire. Does this sound good?
So you have a 125A subpanel out in the shed. It sounds like that subpanel has a main breaker of its own. There's no requirement for a main breaker in a subpanel, but since this is an outbuilding, there must be a master shutoff switch in the outbuilding right where the panel is. Using a main breaker panel is a cheap and easy way to meet that requirement.
You also say you have changed that 125A main breaker in the subpanel to 60A. It doesn't really make a difference what size the main breaker is in the subpanel.
Now this must be fed from a breaker in the main panel. (or not.) Breakers protect wires and equipment. So the breaker in the main panel must be the lowest of
- The breaker required to protect the subpanel apparatus - and that's not really necessary since it has its own main breaker to do that job.
- The breaker required to protect the wiring between main and sub. That is easy; since you have installed 10 AWG wire, your breaker must be 30A.
So the feed breaker in your main panel must be 30A rating.
Now, if you had run #3 copper or #1 aluminum or larger, something neat would happen. Since those wires have the same capacity as your house's main breaker, they wouldn't need a separate breaker and could be lugged straight through.
In the subpanel, neutral and ground must be totally separated, and have separate busbars, because each circuit will need to attach its neutral wire to the neutral bar, and the ground wire to the ground bar. Get one that has separate neutral and ground bars. The big-box cheapie panels make you buy this separately, which defeats the purpose of buying a cheapie panel.
You need to run a ground back to the main panel. Since this is an outbuilding, it also needs a legal ground rod also. These two things (ground wire and ground rod) are there to solve different problems and you need them both.
Lastly make sure the cable you used in the conduit is UF or other outdoor/wet-location rated cable. Using NM (Romex) in outdoor conduit is not allowed; conduit is presumed to be full of water at all times, and the insulation and/or jacketing on the cable is expected to provide the watertightness. Correct is UF cable.
Inside conduit you can also use individual wires. These take less space in the conduit which means you can fit larger wires in the conduit. They are also much easier to pull.