What transmission should go behind an LSX for a $2000 Challenge car, and do piggyback controllers count against budget?

Here is what the documentation says. Each point links to its source; details depend on your exact computer, harness and transmission.

• The Terminator X Max ECU provides four configurable inputs (12V, ground, 5V, frequency) for trans-brake control. (Holley)
• The US Shift Quick 4 ships preloaded with a 4L80E calibration; using it with a 4L60E, 4L65E, or 4L70E requires loading the 4L60E-family calibration. (US Shift)
• For carbureted or mechanically injected diesel vehicles the Quick 4's orange 5V TPS supply wire must be installed, but it must not be installed for EFI applications where the engine ECU already supplies TPS power. (US Shift)
• The Quick 1's built-in user interface shows live sensor values and allows manual shifting; firmware 3.0 and later adds basic self-contained tuning via the tuning menu, with PC software available for advanced tuning. (US Shift)
• The TCI EZ-TCU supports GM 4L60E/4L65E/4L70E transmissions built prior to 2009, all 4L80E/4L85E transmissions, and TCI 4x and 6x transmissions. (TCI Automotive)
• The TCI TCU 2.0 kit uses T-Com 2.0 laptop software with two selectable shift modes, diagnostics and data logging, CAN/BUS compatibility, paddle/button shifter support, and 12 programmable outputs. (TCI Automotive)
• The EZ-TCU setup wizard walks through initial setup including TPS calibration. (Static)
• Chevrolet Performance kit 19332775 covers GM 4L60E/4L65E/4L70E transmissions from 1993 to 2008, while kit 19332780 covers 4L80E/4L85E transmissions from 1991 to 2008. (Gmspecialtyvehicles)
• The CompuShift controller supports GM 4L80E, 4L85E, 4L60E, 4L65E, and 4T80E transmissions, plus Ford AODE, 4R70W, E40D, and 4R100. (Phoenixtrans)

Confirm against the instructions for your exact parts before wiring. More: Transmission control in our tuning guide.