Teensy
The Teensy Microcontroller is a very powerful 32 bit microcontroller (ARM Cortex) with a large number of input outputs. The website of the product is for instance https://www.pjrc.com/store/teensy41.html
Teensy for data acquisition
Bernd Ulmann created a Teensy data logger (Software oscilloscope) which is released as open source at https://github.com/anabrid/TeensyLogger. It is suitable for data acquisition of The Analog Thing.
The usage is basically that the Teensy does the analog to digital data acquisition and then sends (more or less) raw data to a connected PC over USB. It is up to the PC to display and render the data, and no software exists yet (but it is easy to come with).
Limitations: The ADC has only about 10 bits.
Rebuild the THAT-CMOS level shift
If you want to rebuild the level shifting circuit of Bernd with some cheaper OPAMPs, for instance the LM32x series, you should use TTL 5V to power the opamp, since it's not rail2rails: