We have a newly-built 12x36 shed/outbuilding on our property.  Wife and I bought it to turn into a schoolhouse (we homeschool our kids) and a craft/hobby area.

Read some online tutorials and several DIY books on home remodeling, etc.

Basic plan is for 3 circuits.  One line, 15 A for two single-switch overhead lights.  One line, 20A for two grounded electrical outlets.  And finally an additional 20A line for a 7500W window AC unit. (Interior space of shed is 12W and 28L, gambrel ceiling w/ a short loft at either end.  Open ceiling, going to insulate walls and ceiling with corning pink.).

Books I've read have made wiring setup pretty straightforward.  I've finished an empty basement before, added four or five breakers to existing box and wired the whole thing.  No real problems when I did this.

For the shed, I have an existing barn with a 200-amp breaker box (box only has some lights on it now, everything else wired into it is no longer in use--heaters, conveyor system for chicken cages, fans, etc.  Only two breakers used now, one for overhead lights and one for a single grounded outlet.).  From what I've read, I could disconnect a bunch of the unused wiring (maybe switch out new breakers, originals are 25+ years old) and use some of the breakers to run power out to the new shed (rear corner of shed is twenty feet from front corner of barn).  Or I could put a sub-panel in my shed and run a line to the barn, connect into the main panel with terminal lugs. (This seems the most straightforward option).

I've mapped my circuits and power usage, don't think I'll go over 40 amps even with AC and a couple of fans going, maybe a computer or sewing machine.  Even figuring lights, AC and small electronics on both outlets I'm still under 40A.  From what I've looked up online and in DIY manuals, it seems a small 100 amp breaker box, w/12 slots would suffice.  Like I said, i'm planning on three breakers, lights, two 20A outlets and a 20A outlet for A/C.

The two DIY books said 10-3 outdoor would work with 40 amps, to be safe I was going with UF-B 6/3AWG underground, but I think I'm going to run it above ground with a supported line.  

I know this is a wall of text, hoping I was pretty clear in what I want to accomplish.  If anyone w/electric experience would care to chime in, please do.  Thanks.

Consider consulting your municipal building code official.
Pull a permit and take his/her advice.
The code official will respect you for doing the right thing.

If you don't pull a permit, it's likely they'll find out eventually anyway,
You don't want to be recognized by the code enforcement official under that type of circumstance.

I would go with buried conduit with thwn instead of using uf, and a subpanel.

If it is a detached building it can only have a single circuit without a sub-panel.
A sub-panel in a detached building requires ground rods AND a run ground with the power.

Plan on just using buried conduit and pulling wires.

At least you can easily replace the wires if you ever get a lightning strike.

Put in a bigger panel then you think you need.
At least then you can consider HVAC equipment (like a heat pump).

I'm planning on a 100A box, one 15A for the lights, one 20A for two outlets and one 20A for the AC.  That's still around 30amps with everything plugged in/turned on.  6/3 will handle up to 60A, so I should be set.  Not thrilled about burying conduit, never done it.  It's about 20-30 feet, I'm willing to do it if necessary.  Flexible (armor) or solid metal conduit ?  Should I have the conduit come out of the ground and connect to a junction box to keep the ends weatherproof ?  It's things like this where I'm not seeing a lot of ideas online.

Was planning on a copper ground rod/line as well as grounding the lines.  Not going to ever go beyond a few lights and outlets, no central AC or heat.  It's a shed.

Nothing wrong with going overhead, but you will need a rigid metal conduit riser for that.  Quite a bit of work if you want to do it right.   And you will be using a 6-3 plus ground (4 wire) either way.   Prolly AL wire,so put it on a 50 A 2 pole at the barn.  If there is an unused 50A 2P in the old panel use it.

Use pvc conduit and 90* sweeps coming up the buildings,  then a LB going into the sheds panel.  You can use copper ground rods but galvanized work well also and much cheaper

Unless you demonstrate (measure) less than 25 ohms you need two rods.

The problem is always that showing 25 ohms or less requires driving another rod.
You can then remove the rod.
PITA

The limit is two rods without measuring, so just put in two and call it done.

Trying to save a few dollars on something you life may depend on on is false economy.