Noob question about brakes

I know almost nothing about bikes. As I'm prioritizing my mod list for the Grom, I find myself wondering about the brakes. I am surprised how weak they are, and I'd like to improve that. From what I've read, a good set of brake lines will make a world of difference, even on the stock brakes. What I'm wondering is, how much of an upgrade would the Brembo setup be vs the stock Nissins? Will those brakes be noticeably better for the regular, in-town riding I do? Or is that overkill? I have a full Brembo setup on my car, so I know they are great brakes, and eventually I'll put them on the Grom, but is that something that will be worth doing sooner, or can I push it down my list of priorities for the time being and just do the upgraded lines?