Projection systems are odd creatures. In my own experience, they will rarely produce crystal clear results. And you may even find that depending on what is happening with hardware, you will hit walls you never dreamed of. Let alone, know how to overcome!
For example, I've got a fairly recent laptop. I was about to present at a conference. The only connection I have on my laptop is HDMI. If I connected the HDMI cable to the laptop and ran it directly to the device, all was picture perfect. But there were two projection systems. And an HDMI splitting device that was used. The moment I connected to the splitting device, the projection systems messed with the signal and a bright pink hue was introduced and made the screens unreadable. I ended up borrowing a different PC to do the presentation.
I'd say that the first thing you need to do is to identify the resolution of the projector. That will give you the information you need to create the video at the same resolution. And that should produce the best results.
I'm sure others will chime in here with better advice.