Zandronum

Since my computer is capable of HD graphics, is there a way to change the Display settings on the Doom games to make it look all optimized and not all pixelated?

Like what kind of filters, textures, or other settings do I need to use especially running on Zandronum?

Use texture filtering in ogl

http://wiki.zandronum.com/Configuring_Zandronum

Select OpenGL, then find your way into the Display Options, and edit your OpenGL preferences there (like texture filter mode, etc etc)

Don't forget to set your resolution in the "Set Video Options" menu

Note: Adding texture filtering to pixelly sprites and textures like Doom has can make things look horribly ugly, in my personal experience. If you want higher-quality graphics for Doom, you're probably better off hunting for a "high-quality" texture pack; I think Doomsday has some.