What is the best product for Web Banners

I think for a more complex  animated you can  use Animate CC, will be much better,  but  in the 3d canvas. For more smooth animation you can use GSAP, also known us Greensock. Here ( https://www.adsspirit.com/  )you can see  some ex for both type.

You might find this video tutorial helpful Web Motion for Beginners: Create an Animated Banner Ad

Most people in this forum are going to say Photoshop.  I certainly can't think of anything better.  The advantage Photoshop has over things like painting applications, is that it can be very precise with positioning.  In the little contest we had to design the banner for this forum, we were able take the text overlays into account by placing Guides.  Indeed, wee can make a template for things that might be used multiple times, like a FaceBook banner, or we could save a Guide layout.  We can take blend modes into account so we know how it will look when placed over other graphics.

It's Photoshop in its element doing what it does best.

[EDIT] Louie, fyi Nancy does this stuff for a living, and is pretty good at, so give her answer maximum weight.