As a fellow (temporary) Illinois resident that takes multiple trips a year out west, I can say that the large majority of the gear used to chase Illinois whitetails isn't not really well suited for hunting out west. This even pertains to really good top end Midwest hunting gear, most of it isn't designed with the intent of moving lots. A great example is the Sitka whitetail line of gear, its designed around short hikes and comfort in a treestand, more insulation because you aren't active. Having used and abused things like the Sitka Whitetail Bucket in the East and West it just wasn't meant for the application and I bought a Mystery Ranch Metcalf after one hunt with the whitetail bucket out west. A really active Illinois hunt might rack up 2.5 miles including moving treestands and checking trail cams on foot, while a day antelope hunting in Wyoming has always broken 15 miles on opening day for me.
If you are gonna go west Wyoming Antelope is the no brainer as far as costs and logistics go. That hunt can be done for about $600 in tags, gas and food from Illinois once you have filled some capital gear costs. Coming from the Midwest to hunt the west you are gonna spend a few thousand dollars getting up to speed on the equipment needed for hunts. This once again points towards antelope hunting because its cheap, that $1000 elk hunt everyone does the math on doesn't really hold true on your first couple of trips because of gear you need to buy that might be good for 20 seasons.