First of all is a 100 amp panel sufficient?
Usually fine, yes.
Will only be lighting and general outlets because it is going to be a horse barn.
Assuming LED lights, 20 amps would suffice in all honesty.
No heavy equipment.
You could comfortably run most power tools and a shop-vac simultaneously without tripping a 20 amp breaker. I do it all the time with my miter saw + show-vac or table saw + show-vac.
Secondly just want to make sure my math is correct. I believe I can use 1/0 copper in an 1.5 inch schedule 40 pvc.
I don't know electrical math once you get into those sizes.
Consider aluminum like the other posts suggested and consider running a 200 amp wire instead just in case you find that a 100 amp panel is insufficient in the future.
Well pump will be 240 Located in south Florida
These usually require 240v, so you lied about "lighting and general outlets"?
You'd want at minimum whatever the well pump draws plus 20 amps.