I am beginner to this program and I was wondering if I should use inkscape or Photoshop or Illustrator or gump to make my character sprites.
For 2D sprites, Photoshop as is the leading graphic design software. It also allows strong control and manipulation of pixels. Many people use Photoshop because it just works and there are heaps of tutorials over the internet on making 2D sprites with it. However there are many other free pixel art editors which you can use.
For 3D sprites (I’m assuming your referring to 3D models), Blender is a free open-source application which allows you to design models and texture them. However, if you are looking to make pixel style 3D models, Magicavoxel is the best way of creating models like this.
Hope this helps.
I would recommand Photoshop aswell for 2D sprites, except if you want to do pixel art, then you should take a look on piskel site (works on your web navigator and standalone)