I'm not necessarily the best source of info for that. I've only run straight water through mine and use a TLO soil and compost tea supplementing by hand to provide the nute.
I believe
@pop22 uses Autopots so might be able to chime in with his thought on nutes for that system.
That being said, I'd say any kind would likely work but you would want to figure on something that's the least likely to clog up the lines. So I'd personally stick with liquids and avoid the granular stuff unless you're really, REALLY sure it's going to fully dissolve. Hydro nutes may be better suited as they are likely already engineered to not clog stuff up. I think there's also additives on the hydro side specially for preventing line clogs, but couldn't swear to it.