Free: Contests & Raffles.
Did you glance at the pamphlet that came with your application? It has the odds in there for last year.
I think the most obvious, and likely to draw would be one of the Missouri Breaks units. Outside of those, I can't think of too many that are really worth putting in for in order to archery hunt. The Sweetgrass Hills are really cool, don't have huge elk, and is a mix of private land. Bears Paw Mountains would be a very tough draw, and not easy access either. Some of the Lewistown area units have good elk hunting, but again, access can be difficult.If you just want to keep it simple, shoot for the moon on the LE permit and hunt a general unit. Or, hunt the breaks. Both of these options give you some flexibility.
Just know there are not going to be many people with more elk points than you since it just started. Are you wanting a public lands hunt or a landowner DIY hunt? Some areas like where I hunt around Canyon Ferry lake went to a brow tined bull several years back so now you mostly see spikes and raghorns. Alot of areas are hit hard opening weekend(rifle) and tail off later in the season. I like to hunt in the Thanksgiving time frame when it's cold and better chance of snow.