I went through this thought experiment a few months back when we lost to Tech.
To me, the minimum requirement for whoever we hire next should be that they have won a conference championship (or co-championship) at the P5 level in the last decade or so. This shows that they are capable of taking a program to some modicum of success, while playing against solid competition week-in and week-out. Additionally, both of the G5 coaching hires we've made in the last decade have either been mediocre or terrible, so we should avoid hiring directly from that level if possible.
I selected 2010 as the cutoff point for this list, as it was the start of the dark ages that UT Football currently finds itself in. This narrows down the list of potential hires to a little under 30 names:
From this list, we can remove anyone is currently experiencing success at a powerhouse program, has been part of a major scandal, or is seemingly retired from coaching. These coaches would likely not be interested in coaching at UT, or inversely UT would not be interested in hiring them. That gives us the following names:
From these 13 names, I think it's also safe to remove anyone who has not experienced some amount of success recently. Again this is subjective, but for my definition of success I'm going to say the coach needs to have won at least 10 games in a season in any of the past 5 complete seasons (2017-2021). Coaches that meet this requirement are as follows:
There's still quite a few stinkers on this list (namely Malzahn, Helton, and Franklin), but it should at least give us a starting point on who we theoretically should be going after if Sark gets canned. To me the best names are the coaches from the Big 12; Gundy, Patterson, and Aranda. If Sonny Dykes wins the Big 12 this year or Chip Kelly wins 10 games at UCLA this season they should also be under consideration.
TLDR:
The next football coach UT hires should have won a conference championship since 2010, and won at least 10 games in a season since 2017. Based on that criteria, the best options seem to be Mike Gundy, Gary Patterson, and Dave Aranda.