Check out alt-tuner: www.TallKite.com/alt-tuner.html
It's a midi effect that works in your DAW. It does just intonation, all meantones, well temperament, adaptive just intonation, etc. It does 19-tone equal temperament, also known as 19-EDO. It does every EDO from 2 to 72 just by moving a single slider.
If you want to use a QWERTY keyboard, most DAWs let you do that, but even the cheapest used midi keyboard is much easier to play. It doesn't matter how it sounds, the computer will make the sounds.
For 19-EDO, there are two basic approaches: One is to limit yourself to accessing only 12 of the 19 notes at a time. Alt-tuner lets you change which of the notes you're accessing as you play, using keyswitches on the outer octaves of the keyboard or on a 2nd keyboard. You can also use footpedals.
The other approach is to change the usual keyboard layout to access all 19 notes. You will still have the usual 7-white-plus-5-black arrangement, but you tell alt-tuner you want 19 notes per octave, so that C4 (middle-C) up to G5 is one octave, G5 up to D7 is another octave, C4 down to F2 is another octave, etc. All the intervals become much wider, a fifth is almost as wide as an octave. It's definitely harder to play, but not impossible :)
You can take the second approach further by modifying a midi keyboard to a 7-white-plus-12-black arrangement. This is easier than it sounds, the keys just pop off. You must check this out!!
Just to be clear, rearranging the keys by itself doesn't change the tuning, you'll need alt-tuner or Scala to do that.
If you don't have a DAW yet, don't use GarageBand! You will outgrow it, and you won't be able to export your midi, and you'll have to abandon all earlier work. Get Reaper, it's cheap and fast and powerful. For sounds, if you don't have any VSTi's yet, get SampleTank Free, a good starter set of sounds. With this software you'll be able to play and hear yourself live, also record yourself, edit yourself, overdub new tracks with different sounds, etc.
You can also do 19-tones-per-octave tunings which aren't EDOs, like extended meantone. All the above applies to this too. Google "cembalo cromatico" to see 19-tone keyboards from the 1500's tuned this way.