Cow tags usually have less demand, partly why they are cheaper. Harvesting cows does more for population control than harvesting bulls, so departments have objectives to reduce, sustain, or slowly encourage population growth which will set how many tags are available. Bull tags are more coveted, and they're doled out for more revenue vs. what the population can reasonably endure based on success rates. Also depends on if the state/zone is being managed for quality/quantity or opportunity.
Someone may correct me if I am wrong, but I believe it is 15 per application in WY. Any species/sex drawings you enter incur that charge for each application. I'm not 100% sure because I have only been building points there.
For opportunity on elk, if you haven't been playing the game long, Idaho and Colorado are (at this time) good choices. OTC tags are available, though recently have had zones(units) and allocations reduced, from all signs they will be gone in the future. If you don't plan to start playing the game in the systems, I'd suggest looking at those two soon.
Montana you can get a general tag almost every other year currently, not a terrible option.
NM (like Idaho) doesn't have a points system. Although your odds are low you've got a chance to draw. Just not something you can plan on getting often/reliably.
As for telling you what to pick and choose, that's hard to do. It's up to you to decide where and what you want to hunt. You can start by applying for Wyoming antelope, Colorado Elk/Mule Deer, Montana a combo elk/MD hunt, etc. Just depends on what appeals to you.
There are a lot of resources and overviews of how certain systems work and the opportunities. Randy Newberg has some decent stuff on YouTube, you could spring for GoHunt, search through forums for information like here and HuntTalk - these questions have been asked over and over so you should find them through a search petty easily.