Chemical fertilizers are your friend. Everything is in the universe is made of "chemicals", including organic fertilizers. Plants don't know or care if that ammonium ion came straight from air (through the amazing Haber chemical process) or a rotten fish. Nitrate is nitrate. Phosphate is phosphate. Chemical fertilizers are immediately available, and completely adjustable. Once the nutrient is absorbed into the root, " organic" and synthetic nutrients perform identically. Anyone who claims differently is deluding themselves.
Pesticides are a completely different story, I'd definitely stick to organic, if absolutely necessary.
Not that organic doesn't work, but really more of a long-term thing to get the benefits. The <3 months your plant will be alive isn't enough to establish the dynamics of a healthy organic soil, imo. But ultimately, comes down to preference. I find chemicals to be pretty easy, but I'll also throw in some fish emulsion or kelp now and then.