First up, what plugins are you using?
If you're using a soft plugin, forget about trying to make it look better. That's how it looks like on a real PSX. It looks worse on a monitor because your monitor has MUCH MUCH higher resolution compared to your TV, plus your TV has scanlines that mask all the pixelly/blocky textures.
Now if you're using a nice 3d card plus a 3d-accelerated plugin (Glide/OpenGL/Direct3D), then be ready to kick the real playstation's a$$. If your card supports FSAA, enable it and also enable filtering without sprites in the plugin. If not, enable filtering with sprites in the plugin you're using.