Unfortunately the days of "building points" to obtain premium limited elk tags have all but come to an end. Especially for new entrants.
Just as a few examples....if you started applying in Colorado from scratch today as a NR, you're looking at 80-100 years to draw the highest-demand units (ex 2,10,201) and 30-50 years out to draw the modest-demand units (ex 61,76) all of this due to rampant point creep issues. Arizona maybe not quite as long a wait, with their top hunts at probably 40-60 years out for a NR. For Utah the wait would be pretty close to indefinite for the top hunts. New Mexico has no point system, but NR draw odds on the highest demand hunts run in the 1-2% range, in other words a 50-100 year wait on average. Nevada has a bonus points system for elk, but with super slim odds due to extremely high NR participation in the draw. Idaho has no point system, but very few limited hunts.
The good news is you can hunt elk every year as a NR in Montana, Wyoming, Colorado, Idaho. Or you can buy landowner tags in NM, CO, NV. And fundraiser tags in UT. Before getting trapped in the points game, consider simply making plans to get an OTC tag, General Season tag, low-demand limited tag, or simply buy a tag, and then go hunting. Good luck with your plans.