yeah, I would run all wire, and plumbing first, which would be pretty inexpensive (relativley)
also might want to make sure you run good quality RCA or Composite or HDMI cable for your projector (this might be the most expensive part, as without knowing your set up you would need atleast a 6 M cable)
after you have wire and plumbing done you can dry wall.
Depending on the heighth of your ceiling in your basement I would strongly recommend submitting plans and getting a building inspector to signoff, you could increase your square footage significantly.
once building inspector signs off on rough plumb and wire, then drywall.
since this may be a ongoing long term project I would ask how long building permit is good for, you may have to submit several.
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