I think it would be best to concentrate on either pronghorn or deer. Trying to find a good public land hunt where tags are easily drawn for both species may not be impossible but it would be close to it. The demand for Wyoming tags has skyrocketed thanks to TV shows and internet forums that tell everyone how easy it all is. It used to be easy.
The better Wyoming hunting units take either preference points or amazing luck in the draw. You can obtain (buy) one preference point a year for each species. You will probably enjoy Wyoming more if you start collecting points and consider deer and pronghorn as separate hunts. The easily drawn units are normally very difficult public access which makes the small amount of public ground very crowded. Everyone seemingly has a chip in their GPS or app on their phone that shows all of the legally hunted land so there are no secrets anymore. The applicants with the most preference points are the first in line for the better units.
It is possible to get a tag in the general draw without points. A percentage of tags are issued at random but the odds are usually very long for good tags.
Pronghorn hunting advice on the internet is easily found, and very often bad. Everyone that has done it once (or watched the TV show) is an expert. Once you have identified a potential area a phone call to the good folks at the local BLM office is not a waste of time.