I took my wife and son last year in the Laramie valley. We all got tags with zero preference points. We hunted walk in areas, BLM, and HMAs. All three of us shot bucks on opening day (in the snow for a change). two bucks were high 60s and mine was mid 70s. We were out just for fun and not really trophy hunting as it was their first hunt out west. If we had held out, I know we all would have shot mid 70s bucks. Save your points for area 55/60/ or 61. Call the Laramie office game and fish and they will point you in the right direction where to hunt. It's seriously pretty easy and a guaranteed draw with zero points. Like others have mentioned, apply 1st choice for the red desert and second choice where I am talking about.
Of course in your shoes, I would take the guy's offer above. You can't beat a free guide!