at the elemental level it does not matter. the tree huggers will probably argue differently.
3 part allows more versatility in nutrient combos than two part
I used to use GH 3 part flora series. It has always worked really well for me. it gets expensive when you start growing larger gardens so I've switched to other things.

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Also, do the organic nutrients tend to clog hydro systems?
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Yes........

1. Organic vs. "Regular" or whatever you want to call it... mostly preference. If it's important to you to have organically grown plants then sure, go that route. Otherwise I'd advise skipping it. As you say, organics are more likely to clog unless they're very high grade.

2. Again, this is largely preference. A 2-part can be simpler to mix but has less versatility as grizzman points out. I find that three parts last longer because the extra division of contents permits higher concentrations to be shipped. The bottles can be more potent.

3. Currently I use Advanced Nutrients. That's my favorite stuff so far.