Eric, I think Utah is a worth while state to put in for. There are enough good rut elk hunts (rifle, muzzleloader and archery) that the points to draw some of the mid tier hunts has actually stabilized at around 10-14 points. Some of those units are only ticking up one point every 4-5 years, so you probably can get a tag at around the 15 year mark (just so you know what you are in for). The best tags you will never catch, but if you would like to hunt a 310-330 class elk I would put in for those mid tier hunts. You may as well apply for a tag as for a point since you don't have to front the tag fee (it will be billed to your credit card if you draw), and you pay the same application fee if you are applying for a point or for a tag. Utah is a hybrid bonus point state, so you can draw with less than max points.
You will need to buy the hunting license and as Elkhunter96 mentioned, the license is good for 365 days, so if you buy it this year and apply, just so you apply next year before the date you applied this year, you can use the same license. That way you get two years of applications on one license. I expect that option will go away at sometime though.
All of the limited entry deer hunts are very difficult to draw, just because there are so few tags, so you will just have to decide if the extra $10 to apply is worth it. My wife drew one last year with 2 points, it was an 80:1 long shot.
If you apply for sheep, goat, moose or bison, you are basically just buying a lottery ticket, the odds are very very long.
I may be worth buying a general season deer preference point. Utah just stopped their general season, and put all general season tags on a draw. My guess is in 5-7 years there may be some descent general season deer hunting there.
So really it comes down to if chasing the elk tag is worth it to you. Like Zim mentioned, you could just save the money and buy a landowner tag somewhere too.