there's a small paperback book that we've used in it's various updated editions for the last 35+ years. it's called "Wiring Simplified" by Richter & Schwan.
the current edition is http://www.electricwiring.com/wiring.html
you can usually find a copy hanging in the electrical dept of a Lowes or HD, priced at < $10.
it's a handy tool and reference for designing or spec'ing a project like this the right way the first time.
besides sizing your wire or conductors, and conduit, the book will also help you with things like how many bends you're allowed in your conduit before a pull box is required, and limits on the length of conduit before you need a pull box, and burial depth.
another handy item for your project might be a bottle of "pulling lubricant". it's amazingly helpful stuff, even when you're pulling short runs.
IDEAL INDUSTRIES, INC. - ClearGlide™ Wire Pulling Lubricant
if you were going to hand dig that 150' trench, think about renting a machine or hiring your local sprinkler guy to trench for you, instead.
a 150' x 24" trench with a machine will be reasonably straight with a consistent depth, and depending on the soil conditions, take only about an hour to complete.
"Direct Burial Warning Tape" placed into your trench, 6-12" below the surface will also help prevent future problems from an errant shovel....
lastly, you might also consider burying telephone & coax cables alongside your conduit, or, placing a second, empty conduit for future use.
work safely, and good luck with your project!