Your fluorescents will do OK up to about a 6" plant. Also when you first put outside, you might want to partially shade with white plastic, to reduce danger of shock, until the plant adjusts to the higher levels of light intensity. You might place in a south facing window to harden.

Good advice.
Never got into "grow lights"...I grow too many plants.
This is my reminder page and may be helpful Starting from Seed.
It's an attempt to be helpful to others,but it's not fully explained because it's like I said "a reminder page".