Electrical – Running Electrical to a Shed

You have the right general idea

The rigid conduit is fine -- you will only need to dig 9-12" down for this, and a 2" RMC or EMT provides plenty of space to make for an easy pull and future expansion. Furthermore, the metal conduit provides the equipment grounding conductor to the shed, which saves you a wire in the pull (two black hots and one white neutral is fine). Also, finding a 60A breaker for your meter-main isn't an issue -- a THQL2160 will do the job, and should be available anywhere circuit breakers are sold.

You still will need ground rods at the shed though

You will need two ground rods (minimum 8' long and 6' apart) at the shed, with a 6AWG copper wire from there to the shed subpanel ground bar, though. This provides a path to ground for lightning induced transients, while the metal conduit returns fault current back to the service entrance (aka its source). As a result of this splitting of return paths, you will also need to ensure that the bonding screw or strap has been removed (or was never fitted to begin with) to the subpanel, and will also need separate neutral and ground bars there.

Other notes

You should use an inch-pound torque wrench or torque screwdriver (depending on the torque setting called for) on all breaker and panel lugs to torque them to manufacturer specifications -- this improves system reliability vastly, and is also a new requirement in the 2017 NEC (110.14(D)).

Also, the shed subpanel will need to have a main breaker in it to serve as a disconnecting means for the shed. It is OK to use a big main breaker here, though, since the upstream 60A breaker in the service-entrance device will protect the feeder wires from overcurrent. As a result, the simplest way to go here is to get a 100A or 125A, 24- or 30-space, main breaker panel and fit it with ground bars if it doesn't already come with such. That way, you will have plenty of space for expansion -- if you want more current to the shed, you can swap the feeder breaker and wires for larger ones, and you can also add circuits fairly freely there without worrying about running out of breaker spaces.

That's fine. The breaker protects the wire, and it's always allowed to use larger wire than you need, so bumping the breaker down to 15A is legal. Based on your anticipated load, it sounds like you won't have a problem with the breaker tripping.

The one issue you may have is if you intend to run a space heater on one of the shed outlets sometimes -- they usually use a whole 15A circuit by themselves, so that wouldn't be compatible with also having the lights on the circuit. However, that would just trip the breaker and wouldn't present a safety issue.

Note that since you have pool lights on this circuit, it'll need to be GFCI protected. If your current 20A breaker is a GFCI breaker, replace it with a 15A GFCI breaker. If it's a normal breaker currently, you probably have a GFCI somewhere downstream (though check this, and rectify if not), so replacing with another regular breaker is probably okay, but doubling up on the GFCI is allowed, so you're welcome to use a 15A GFCI breaker in either case.