The Big 12 will expand this season, taking in my opinion 3-6 teams (depending on whether Missouri leaves or not) and will soon have 12+ members again. This means an 8-9 games conference schedule. Any expansion candidates must consider this schedule, leaving only 2-3 non conference games available. Some of these non-conference games must include games against national and regional rivals. Regional rivals are particularly important to establish a regional presence to build both a fan base and capture media market. Local fans are the most important as they will attend games, buy team related products. A large local fans base will also force more media attention and service.
The leading candidate so far is BYU. BYU has the largest sporting presence in Utah as well as a national presence. Their non conference games would include Boise State, Utah, and possibly one other. These regional non-conference games will certainly help BYU to deliver Utah.
If the Big 12 wants geographical continuity with BYU as well as regain the Colorado market, it must consider a Colorado program. Colorado left the Big 12 for the Pac 12 will not be coming back. That leaves the Air Force Academy or Colorado State. The available number of non-conference games almost certainly rule out Air Force Academy. Air Force will want to play Army and Navy each year. Air Force has also been a frequent competitor of Notre Dame. For Air Force to grab the Colorado market, it must also play against instate rivals Colorado and Colorado State. This is particularly true for Air Force because despite being in Colorado, it neither recruits nor serves Colorado. Both Colorado and Colorado State thus must be a part of the non-conference schedule. Playing both of these Colorado teams along with Army and Navy just is not practical. On the other hand Colorado State non-conference schedule would include the biggest sporting event in Colorado when it plays against the University of Colorado. It would also highlight a Big 12 vs Pac 12 rivalry (similar to a Iowa State vs Iowa game). Colorado State other rivalry with Wyoming would also help deliver the Colorado market. My analysis would favor Colorado State rather than Air Force for the Colorado market.
Another populous state with potential for cross conference rivalry is Louisiana. Here I think Tulane is our best option for the Big 12. Tulane is an AAU member. Tulane is a well established institution in New Orleans and a historical rival to LSU. True Tulane is not very competitive on the field but teams get better by playing against good teams regularly (which the current even shrunken Big 12 has plenty of) and by investing in its athletic program financially. Being a part of an Automatic Qualifying conference will bring more experience and money to Tulane. Given that Tulane is fairly well established in academics, there would be less of an issue for Tulane to put more money into Athletics. Tulane's non-conference rivalries with LSU and Southern Mississippi would certainly help gain viewers in the southern Gulf coast region. The alternative program to Tulane in Louisiana is Louisiana Tech. However, Louisiana Tech is not located in a major metropolitan area, not strong in academic, and doesn't have as much of a presence as Tulane. Tulane was recently mentioned as a potential candidate and they should be considered.
New Mexico might be a consideration but this should be a last resort to fill a gap and round out conference membership to an even number rather than a primary or even secondary target for expansion. There are two teams in New Mexico, University of New Mexico and New Mexico State. Neither are academically outstanding and both have equivalent metropolitan area (Albuquerque and Las Cruces + El Paso). Albuquerque might be a reasonable consideration. A better choice for the Las Cruces + El Paso market would be UTEP rather than New Mexico State. New Mexico could have an outside shot at being considered for the Big 12.
UTEP really doesn't add much to the Big 12 that it doesn't already own in Texas. The top 3 teams in Texas are UT, TA&M, and TTU. TA&M is now lost to the SEC. TCU might be a consideration in that it is the only remaining Texas team with a national recognition. However, SMU isn't so far behind and nor is Houston. Perhaps the best reason to take TCU is to deny the Big East a Texas presence. Of the remaining Big 12 states none have any in state options of note. Of the surrounding states there really no viable options either beyond those mentioned above(Colorado State, Tulane, and New Mexico), whether it be Arkansas, Arizona, the Dakotas or Wyoming.
There is the option of raiding the Big East by taking Louisville, Cincinnati, and even West Virginia. I seriously doubt the Big East will fold any time soon. In addition, if Missouri leaves, these 3 Big East programs will be even less attractive. There won't be geographical continuity. Missouri in this sense is the Big 12's gateway east and these 3 school's gateway west.
Looking West there remains Boise State. Though a very competitive football program, unfortunately Boise State doesn't offer much else, whether it be academic, geographical proximity, or regional media market. However, like New Mexico, Boise State will be considered as a filler team.
In summary, my assessment of expansion candidates for the Big 12 are:
Tier 1: BYU (to replace TA&M)
Tier 2: Louisville, Cincinnati, WVU, (only if Missouri stays, and even so, unlikely)
Tier 3: TCU, Colorado State, and Tulane
Tier 4: Boise State, New Mexico
I can see the Big 12 going to 14 for both stability (should another team leaves) as well as parity with the ACC and the SEC. I do not see the Big 12 going to 16 because there isn't a reason to yet, and because when the time come, a 14 teams big 12 will be in a stronger position to take better candidates than it can now. My 14 are: all the current Big 12 (including Missouri), BYU, TCU, Colorado State, Tulane, and Louisville.