That would be Baylor, our oldest and longest rival, and currently, probably the best. We've played the Bears more than any other team (including SMU), we used to both be located in Waco and, even in SWC days, it was always Baylor that we hated. For example, they used to prohibit dancing, so we'd chant "we can dance, yes we do, we can dance, how bout you?" at them. TCU is Christian (Disciples of Christ); Baylor is Southern Baptist. You'll fit right in and will be rivals with both of us easily.
UT is also a rival, but they would never acknowledge it, so it's not the same. Tech is, but they only joined the SWC in the late 50's, so it's nowhere near as historic. We are in the process of developing rivalries with OU and OSU; curiously, we used to play KU every year from the 40's through the 60's, so we've played them A LOT. KSU, ISU and Wva. are all new to us (just like the MWC schools were.)