That should be a SWEET gameroom! Thanx for the pics too, I am a Union carpenter and highly enjoy doing wood framing jobs, which is rather rare in commercial work.
Hanging drywall isn't too bad, but depending on the job you do hanging it will determine the difficulty of finishing it. Less seams is preferred, but more important is do whatever you can to avoid butt-joints. This generally means standing the proper length sheets up verticle for the walls, hopefully the framing is on 16" centers. It looks like you intend to drywall the ceiling too, use 12' sheets for this if you can. There will still be butt-joints, but a lot less than if you use 8' sheets. Also, make sure the screws/nails are countersunk up to about an 1/8 of an inch. Not so much to break the paper, but enough that there won't be a hump to mud over.
For ripping sheets lengthwise, hold the tape measure in one hand, with the sheet upright on it's side. Have your knife in the other hand. Pull the tape out to the measurement you want/ want to cut off. In this example the number is 11"
Then put the blade of your knife on the end of the tape and put against the sheet (the example is plywood) while still holding the measurement and the body of the tape with the other hand.
Hold this while you pull the tape and knife at the same time all the way across the sheet.
It takes a little practice to get a nice straight line, don't try to go too deep the first pass, and once you do, it'll save a ton of time as opposed to snapping a line. Use a 4' T-square to do the full cross-cuts.
I am remodeling a client's basement right now working for myself.