So as a new guy deciding to put in for some tags across the country, what would some of you more experienced guys offer as your top 5 pics for tags to apply for? Regardless of chances, I'm looking for best areas for trophies of elk, and muley mostly, but also want to put in for goat and sheep. So where to start and how to research good areas throughout the country...

For western game, this site has a few things that are incredible
wwww.monstermuleys.com
They have a hunt draw odds calculator, select the state, species, and weapon and non-resident vs resident and they will tell you what are your odds of drawing, I know not exactly what you were looking for, but a very helpful tool nonetheless.
To put it in perspective, I am in Utah and have been applying for my trophy elk unit for 9 years, probably will get it in the next 3 years or so. I have also been applying for a bison tag on the Henry Mountains(one of the only indigenous non-reintroduced herds in the U.S.) for 10 years and still only had a .01% chance of drawing this past season.
In Utah, some of the best muley units will take 5-7 years, with THE best taking 15-17 years.
Wyoming has some excellent units, non-resident area G comes to mind.
Sheep......yeah....expect 15+ years unless you have 30K to buy the tag....
Hope that this helps.

I subscribe to hunting fool magazine:
http://www.huntinfool.com/

This has a lot of the information that you are looking for. Trophy Elk in Utah, I just drew w/17 pts. (17 years). Mule deer in Southern Utah is also world class but many years in the waiting.

Without regard to odds, the best units are as follows-
Mule Deer- Utah, Henry Mtns -- Nevada, 231
Elk- Utah- San Juan --- Arizona, 10 --- Nevada 231
Of course there are other great units, but with the non-resident tag allocations, you will NEVER draw them. Never, under the current systems.

But why would you only want to apply for hunts with less than .1% (that is one tenth of one percent) odds?

You gotta buy deer points in: Colorado, Wyoming, maybe Utah, maybe Nevada. Elk points in Wyoming, maybe Utah, maybe Colorado.

You are wayyyyy behind in the draw odds for higher end, well publicized units.

Justanotherhunter's post is wayyyy too optimistic. The best muley units in Utah take 17 points TODAY. In 20 years those same units will take a non-resident 35 points to draw. Same with the best elk units in Utah. There can be no "time-line" placed on when a guy will ever draw a sheep tag.

As for HuntinFool, we use it to AVOID the areas they recommend. Once they highlight an area the odds go in the toilet and within a few short years the quality of animals goes down the toilet also.