parallax occlusion mapping is pretty much one of the last things you should concern yourself with right now, sure it's neat, but what you need to begin doing is first geometry rendering or making sure your using https://www.thangmmo.com/s and things like that to make it really fast and solid, secondly you need to focus on the high visibility stuff or what is still going to be visible is you stand really really far away from the monitor (or squint with your eyes really hard).
That usually mean lights, shadows and textures.
Beyond that i can't tell you any specifics without seeing the old game and knowing a little about your graphical ambitions (creating a mock-up of what you want in blender/lightwave/maya/max will help you a lot with that).
But in general for the generic 3d game i would today recommend deferred rendering with depth shadow maps and post process filters (you can skip the deferred part if you only use one or two lights or have very basic lighting).

The most important bit is to take it one step at a time, preferably without breaking the rest
So
1. get the geometry sorted out first
2. figure out how the lights are going to work individually and accumulate them into an FBO
3. make sure all of the different parts are up to date (you wouldn't want your textures to suffer because your not using anisotropic filtering)
4. try and make it all work together at once, the way you know this is done is when you have an elegant solution with few or no workarounds.
5. now you can do stuff like parallax mapping

Another thing you do need to take in consideration is that a game will look better if it plays better so it would be wise to work on improving the gamecode over all and upgrade all parts of it, everything from input handling to physics to AI to sound, try and improve it all if you can that is.
And don't forget to upgrade you actual game data.

But please ask if there is anything specifically (additional information would be great in that case)