Best way to future proof is to run about 5 strings in a 2" PVC pipe. That way you can always pull through whatever cable you might need in the future.
To watch movies from a computer, you need the correct cable for your PJ and computer… if you have an HDMI out on the computer, by all means, use that. If not, then yes, you will need a cable to connect your computer to the PJ.
RS232c is a connection for hardwired system remotes. You may or may not have one now, but I would run that anyways. When you're already at it, also run a network cable to the PJ. More and more, that is the new standard for connecting a systems remote to the PJ, so that way, you're already set if you ever need it.
Otherwise, a single HDMI cable would be sufficient. Make sure you get a cable that can handle the run length you need and is 4K compatible for the future. I order my HDMI cables (and most other cables) from www.monoprice.com
, their HDMI with Redmere works really, really well and they just released a new high-speed/bandwidth cable. To boot, they're quite affordable as well (and no, no affiliation other than a happy customer)