220ft Feeder Run to Storage Shed
Given your requirements, you don't need much for HVAC

For a shed the size of yours, just about any HVAC unit you can come up with will do the job.  The basic tradeoff, then, is "do you want to do the bit of extra work a subpanel entails for a simple storage shed, especially given that the wiring's in conduit and can be easily replaced in the future, or would you rather save some work and perhaps a bit of money now, at the cost of being limited in what you can use for a HVAC unit?"

If you want the cheapest way possible to do this, I would use a 20A, 2-pole breaker in the panel, feeding 4 12AWG copper THHNs (black, black or red, white, green or bare) in the conduit, and then use a reducer to interface the existing conduit to a non-fused air conditioner disconnect at the shed to provide the required disconnecting means.  This means you'll need a 115V HVAC unit, which are rather thin on the ground, though: the Amana PBH092G12CC is what I'd recommend as it's a full-fledged heat-pump in a through-the-wall package (instead of being a simple "air conditioner with a toaster element attached" arrangement).  This is plugged into a single 5-20R that goes to one side of the MWBC, while the other side feeds the light switch/fixture and a GFCI convenience receptacle.  Finally, at the disconnect, all the grounds go into the bonded bar provided, while the neutrals simply are connected together with a wirenut as they need to float.

The alternative gives you a 230V HVAC unit, but requires you to install a subpanel, complete with main breaker to serve as a disconnect, (our advice: go big or go home on subpanel spaces.  A 24-space, 100A or 125A subpanel would not be at all out of place here.) and a grounding electrode system at the shed in addition to the equipment grounding wire in the conduit.  Fortunately, two 8' ground rods driven 6-8' apart and connected to the subpanel with 6AWG bare copper suffices in most places, with a 15A or 20A 2-pole breaker in the subpanel for the single NEMA 6-20R for the HVAC unit and a pair of 20A, 1-pole breakers, one for the light circuit and the other for the GFCI.  All of this would go with 4 10AWG (black, black or red, white, green or bare) wires in the conduit and a 30A, 2-pole breaker for the feeder.  (The size of the subpanel's main breaker doesn't matter since it's just being used as a disconnect switch in this application.)

TORQUE ALL LUGS TO SPEC

There's one other thing you'll want to do here, and that's use an inch-pound torque wrench or torque screwdriver to tighten all the electrical connection setscrews to their manufacturer specified torques.  This is required by 2017 NEC 110.14(D), and also is a good way to make sure your electrical system won't give you the loose lugnut!