RE: Hunt Elk without breaking the bank
Well for ML in Colorado you have ten days to get in your application before the April 6th deadline. Same goes for any of the draw specific units but you won't draw a tag for those for about six years or more.
You can get an OTC either sex archery tag for most of the state. Same goes for rifle season. If you wanted to you can apply for a cow tag in an OTC unit and purchase a bull tag for the same rifle season but that is some extra cost.
You should contact the Colorado DOW and inquire about success rates for different OTC units and which ones are undersubscribed units. The undersubscribed units will usually have more elk and less people than the units that every one is going to.