If you just wish to learn and get your hands dirty, then any embedded platform with a decent C compiler will work. Personally I'd probably focus on one of the ARM lineups, like the M4 series from TI you mention. The reason for choosing ARM is that it is the defacto standard platform across the industry, and you get the most computational bang for the buck in a general purpose embedded MCU. Think we are up to quad core 1.4 GHz CPUs by now?
However I'd also suggest not getting too hung up on an exact choice of platform as you start. You need to get some idea of how much computational power your problems contain, and your initial choice may not survive the harsh light of reality for very long. For instance TI's Tiva MCUs runs at 80 MHz. If you wish to sample at, say, 400 KHz, then that leaves you with an average of 200 clock cycles to process each sample. Depending on the job needing to get done, that may either be plenty or woefully inadequate.