Thanks Bob. I really appreciate it. 
One of the many things I'm struggling with is the difference between the "random draw" and the "preference draw". Are these two separate drawings? Also, is it worth it to put in for the reduced price doe/fawn drawings, or are there enough leftover tags to go around?
I'll try to answer these now. Wyoming has a preference point system whereby if you apply and do not draw a first choice hunt, you accrue one point. You may also purchase a point.
In essence, everyone in Wyoming has one or more points.
The "Prefence Points" draw is run first. Applicants with more points have a greater chance of being drawn, but are not necessarily guaranteed to draw. Seventy five percent of non-resident permits go to the applicants with the most points. For example, assume there is a unit with 100 permits. Seventy-five will go to those with the most points; the other 25 go to the "random draw". Assume there are 50 applicants with four points, and 10 with three points, and 10 with two points. The 50 get permits first, leaving 25. The 10 with three points get permits, leaving 15. The 10 with two points get permits, leaving five in the preference point draw. Since there are no more "with most points" applicants left, the remaining five go into the random draw along with the initial 25. There are 30 permits in the random draw. All applicants that did not draw in the preference point are automatically put in the random draw.
To complicate matters a bit, Wyoming also has a "Special" permit category for deer, elk, and antelope. These are a separate group of permits available to applicants who will pay more if drawn. For example, a regular non-resident buck antelope license costs $272, while a special license costs $512. In most instances the odds of drawing a special permit are better, because there are fewer applicants willing to spend more. You need to look carefully at odds of drawing to see how much better the special license odds are, if you are interested.
Here's a link to the 2012 draw odds. Note there are several categories for each specie. Hopefull they make a bit more sense now.
http://wgfd.wyo.gov/web2011/hunting-1000590.aspxSecond question: using antelope as an example, you can apply for up to two reduced price doe/fawn licenses in the Spring draw (March 15 deadline). All licenses that are not sold in the Spring draw go into the "Leftover" pool which go on sale in July on a first-come, first served basis. A hunter may purchase up to four doe/fawn licenses each season. If you apply for and draw two in the Spring draw, you can purchase two more from the Leftover pool. If you do not draw in the Spring draw, you can purchase up to four from the leftover pool. The advantage of applying in the Spring is that you have a better chance of getting licenses in your desired area. It is entirely possible that all available permits for a certain unit will be sold in the Spring draw, and none will be available in the leftover pool. Most units have at least some leftover doe/fawn antelope licenses, but not all do. Also, note that leftover "any antelope" tags are available in many units as well.
The three primary factors that determine where to apply in Wyoming are areas with: (1) good antelope numbers, (2) good access, and (3) available licenses / draw odds. What that means is that areas with good antelope numbers and lots of public land will have extremely low draw odds. Areas with high antelope numbers and little public land will have very good draw odds (100% in several instances.)
I've been able to hunt public land for many years and find antelope without too much difficulty. Two years ago I shot a 16" buck that was within 150 yards of a major interstate highway.
There are some tricks to the trade.