I'd use a 4/0-4/0-2/0-4 Mobile Home Feeder cable for this job
Given that you aren't going to be pushing a full 200A over the cable (which'd require 250kcmil Al, since the 83% reduction in 310.15(B)(7) doesn't apply to your situation), but need a 4-wire cable as your shed is getting powered by a feeder from your service disconnect at the pole, I'd use a 4/0-4/0-2/0-4 aluminum Mobile Home Feeder cable for this job. Furthermore, while you can direct bury MHF, I'd run it in a 2" PVC conduit instead; this way, if you decide to go up to a full 200A, you can repull the wires instead of having to dig everything back up to replace it.
You are correct on the grounding rods
The good news is that you are correct that you'll need two grounding rods at the shed. A 6AWG copper grounding electrode conductor will suffice for connecting them to the shed panel's grounding bar. Note that if your shed panel doesn't come with grounding bars, you'll need to fit the appropriate grounding bars yourself in addition to using them to land your grounding wires and pulling the green bonding screw out of the panel.
TORQUE ALL LUGS TO SPEC
Last but not least, you'll want to use an inch-pound torque wrench and/or torque screwdriver to tighten the various connections to their specified/labeled tightening torques. This is required by NEC 110.14(D) in 2017 and newer NEC editions, and is a good idea anyway as it'll keep your electrical system from giving you the loose lugnut!