If you want to guarantee you are hunting you should cross off NM, AZ, WY or UT unless you are buying a landowner tag which will cost you big $$. Those states you will have very low draw odds.
Positive on NM is everyone has same low chance no preference points. AZ, UT , WY good units you have to have many many years of points.
The states where you can have a good quality hunt are Montana draw with Guide which your odds are very high or Colorado OTC tag.
Ultimately I would recommend Montana as the elk densities are high, Good Outfitters are plentiful and you don't run into as many other hunters as Colorado. You can get it done with a good outfitter, good lodge, good food for under $ 6K all in including tag, processing, tip etc.
(Tag will cost you roughly $ 1K, Outfitter $ 4.5K)