From left to right, it appears you have oregano, parsley, and sage (rather than basil). I have never tried growing them in water, but it's certainly worth a whirl. All three are pretty hardy. I have good luck sticking grocery store herbs (basil, parsley, cilantro) in water on my kitchen counter, although I am just trying to keep them fresh until I've used them up. Let us know how it goes. And welcome!