I want to run service to a Calf Shed approx 175' from the Main to install a light receptacle also an outlet for a Calf Tank Water Heater, from the calf shed I want to run 30 amp service for two trailers and they are approx 25-30' closer to the main. What I am looking for is the most economical means of accomplishing this issue.

Sounds like a 100 amp subpanel would be needed at the shed. The panel can have a 20 amp circuit breaker for the light in the shed, and a breaker for the heater, size unknown.

Then there can be a 30 amp breaker for the trailers, two if each trailer needs a breaker.

You can use #2 aluminum wire, in a four wire cable called URD, rated for direct burial.

Need to have 6 inch of sand above and below the cable buried 24 inch deep.

Install a warning tape above cable 12 inch below grade.

You may consider using Schedlue 40 PVC conduit and #2 al wire XHHW insulation, conduit offers more protection and allows cable to be replaced later if needed.

You need to consider a equipotential ground grid for buildings and ares that will hold livestock.

http://fyi.uwex.edu/mrec/files/2011/04/document.pdf

This is not all the detail you need to complete this project, enough to get you started thinking.