Unity will allow you to make a demo of your game, faster, but as far as fps games, Unreal 4 + 5, Godot if you want to learn that, Cry Engine and good old Source Engine, from TF2, will allow for competent fps demo and full games. Question is why settle for a PS1 style of graphics? Are you personally nostalgic for that fps era, or trying to sell it to others in that fps aesthetic? All may give you what you want, via plug ins and mods. Look around, and you'll find what you want. Good luck with your project. Personally, I 'd go with Unity 5, and Unreal 4.