Can I just use regular fluorecent tube light for small plants

Basically, Yes! Simply, You need 6500k for veg cycle, and 2700k for bloom cycle.
I use a T5 setup. That is probably what you have that you described as eing 19-20", and that would work in the beginning. In order to grow successfully indoors; One must be willing to invest in the correct lighting, or must temper expectations of yield.