If you are in a situation where you will have good light control, go with a projector, especially since you are after a large picture. TVs are more convenient, and you can get 4K TVs for a reasonable price unlike projectors, but if you are aiming for an 80" screen or larger, projector.
For the projector, since you want to play video games, you will want to make sure it has a low latency picture.
After you have decided on projector, decide on what kind of surround sound system you want. Will you be happy with 5.1 or do you want a big Atmos system with multiple subwoofers? My advice here is don't compromise on the quality of the front stage speakers or subwoofers for a whole gob of surround channels speakers. Also, try to get two decent subs. Of course a lot of this depends on your budget.
For a projector, do not skimp on the projector mount- get a good one. Also, do not overpay for speaker cables, HDMI cables, or subwoofer cables. You can get perfectly fine cables at Home Depot, so do not spend big on Monster brand cables or something like that. If you want to order your cables, use
bluejeans cables.
Lastly, Audioholics has TONS of great resources to get you going. I doubt there is a better site on the internet for this, from beginner to advanced users.
Here is a simple article for thinking about the basics. But there are whole libraries of these kinds of articles here, like
this,
this,
this, and
this. Good luck!
